Contentsweb/@inf/@math/... · Contents Foreword 2 ... Special Sessions 1. Algebra and Number Theory...

Contents

Foreword 2

Conference Organisation 3

Conference Program 5

Timetable of Events at a Glance 7

Plenary Lectures in the Hope Theatre 9

Special Sessions1. Algebra and Number Theory 102. Calculus of Variations and Partial Differential Equations 123. Computational Mathematics 144. Aspects of Applications in Mathematics 155. Operator Algebras and Noncommutative Geometry 176. Optimisation 187. Geometry and Topology 198. Topological Groups and Harmonic Analysis 219. Financial Mathematics 22

10. Combinatorics 2311. Probability and Statistics 2412. General session 2513. Mathematical Physics 2614. Differential Geometry 2715. Education Afternoon 28

Conference TimetableMon 26 September 2011 29Tuesday 27 September 2011 33Wednesday 28 September 2011 39Thursday 29 September 2011 42

List of Registrants 45

Abstracts 510. Plenary 521. Algebra and Number Theory 542. Calculus of Variations and Partial Differential Equations 583. Computational Mathematics 614. Aspects of Applications in Mathematics 635. Operator Algebras and Noncommutative Geometry 686. Optimisation 707. Geometry and Topology 738. Topological Groups and Harmonic Analysis 779. Financial Mathematics 79

10. Combinatorics 8111. Probability and Statistics 8312. General session 8513. Mathematical Physics 8714. Differential Geometry 9014. Education Afternoon 93

Index of Speakers 93

From the Director

I would like to extend a warm welcome to all participants in the 55th Annual Conference of theAustralian Mathematical Society. I am pleased to see that we have been able to attract nearly 240mathematicians and mathematical educators to this meeting, a good number for a conference in anon-capital city. We are especially pleased to welcome delegates from eleven different countries to theconference.This year’s program features talks from a wide variety of areas of Mathematics and geographicallocations. On behalf of the scientific committee I would like to thank all the plenary speakers foraccepting the invitation to speak at the 55th Annual conference. With over 50 students registered,there will be plenty of competition for the B.H. Neuman prize for the best student talk. I wish themgood luck, and hope that they find the conference mathematically stimulating.Following on from previous years, this conference again includes an Early Career Workshop, an Edu-cation Afternoon for mathematics teachers and a Public Lecture – this year the Public Lecture will begiven by Mick Roberts. His lecture: The mathematics of epidemics and pandemics is highly topicaland is indicative of the wide reach of modern mathematics.I am happy to announce that our program includes the second Hanna Neumann Lecture. This year thelecture will be given by Nalini Joshi, the first female professor at Sydney University, former presidentof the Australian Mathematical Society and Chair of the National Council for the MathematicalSciences.Finally I would like to thank all of the kind people who have helped to organise this conference: frommembers of the scientific committee, to session organisers, to all of the staff and students — bothprofessional and academic — at the University of Wollongong who have been involved in various ways.Without your help and support, this meeting would not have been possible. I also wish to thank theDeputy Vice Chancellor (Research) Judy Raper and the Dean of Informatics, Phillip Ogunbona, fortheir financial support for this meeting. I also thank the Australian Mathematical Sciences Institute(AMSI) for sponsoring the Education Afternoon.Specifically thanks, in no particular order. To John Banks at La Trobe University for designing awonderful registration system. We are grateful for all the work you have put in to make this difficulttask much more manageable. To Lisa Pyle, who had not realised when she started in February, howmuch work she had let herself in for. I am grateful for all her help in keeping the local organisingcommittee on task. And to Aidan Sims and Jacqui Ramagge, who have contributed so much of theirtime to make this conference come about.In hope that you all have a very agreeable conference, and that you enjoy your visit to the Universityof Wollongong and to the Illawarra.

David Pask

Conference Director

2

Conference Organisation

Local Organising Committee

David Pask – Conference DirectorAidan Sims – Special Sessions and TimetablesJacqui Ramagge – PublicityNatalie Thamwattana – ECR and Women’s EventsBronwyn Hajek – ECRRuibin Zhang – AustMS representativeCaz Sandison – Teacher’s AfternoonLisa Pyle – Coordinator

Scientific Committee

David Pask (University of Wollongong)Ruibin Zhang (University of Sydney)Ole Warnaar (University of Queensland)Yihong Du (University of New England)Gary Froyland (University of NSW)James Parkinson (University of Sydney)James Borger (Australian National University)Yvonne Stokes (University of Adelaide)Nora Ganter (University of Melbourne)

Organisers of Special Sessions1. Algebra and Number Theory – James Parkinson, Anne Thomas2. Calculus of Variations and Partial Differential Equations – Ben Andrews, Yihong Du3. Computational Mathematics – Bishnu Prasad Lamichhane4. Aspects of Applications in Mathematics – Barry Cox, Georg Gottwald5. Operator Algebras and Noncommutative Geometry – Nathan Brownlowe, Denis Potapov6. Optimisation – Natashia Boland, Andrew Eberhard7. Geometry and Topology – Finnur Larusson, Craig Westerland8. Topological Groups and Harmonic Analysis – George Willis9. Financial Mathematics – Fima Klebaner, Song-Ping Zhu

10. Combinatorics – Alice Devillers11. Probability and Statistics – Mark Fielding12. General session – Aidan Sims13. Mathematical Physics – Gavin Brennen14. Differential Geometry – Michael Eastwood15. Education Afternoon – Jacqui Ramagge, Caz Sandison

This booklet was produced by Ben Maloney of the University of Wollongong in LATEXusing templateskindly provided by John Banks of La Trobe University.

3

The conference organisers acknowledge the financial

support given to them from

The Faculty of Informatics

e

4

Conference Program

Overview of the Academic Program

At this meeting there will be 7 plenary lectures, one public lecture, 183 contributed talks and 14special sessions. The Education Afternoon on Tuesday 27th September features an addition two talksaccessible to a general audience, and concludes with a panel discussion Cave or Tunnel? Is there lightahead?

B Conference Timetable

Mon 26 September 2011 – page 29Tuesday 27 September 2011 – page 33Wednesday 28 September 2011 – page 39Thursday 29 September 2011 – page 42

Plenary Lecturers

Nalini Joshi (University of Sydney)Kenneth Paul Tod (University of Oxford)John Sader (University of Melbourne)Vigleik Angeltveit (Australian National University)George Willis (University of Newcastle)Hiroshi Matano (University of Tokyo)Mick Roberts (Massey University)B Timetable of Plenary Lectures and Public Lecture – page 9

Public Lecture

Mick Roberts (Massey University)

Special Sessions

1. Algebra and Number Theory – page 102. Calculus of Variations and Partial Differential Equations – page 123. Computational Mathematics – page 144. Aspects of Applications in Mathematics – page 155. Operator Algebras and Noncommutative Geometry – page 176. Optimisation – page 187. Geometry and Topology – page 198. Topological Groups and Harmonic Analysis – page 219. Financial Mathematics – page 22

10. Combinatorics – page 2311. Probability and Statistics – page 2412. General session – page 2513. Mathematical Physics – page 2614. Differential Geometry – page 2715. Education Afternoon – page 28

Education Afternoon

Michael Giudici (University of Western Australia)Michael Barnsley (Australian National University)Panel Discussion: Cave or Tunnel? Is there light ahead?B Timetable for Education Afternoon – page 28

5

Conference Program

Social Program

I Sunday 25th September, 16:00-18:00Welcome Reception and RegistrationNovotel North Beach, 2-14 Cliff Road, North Wollongong

I Monday 26th September, 12:30-13:45Early Career Researchers LunchSMART Building, 6.105

I Tuesday 27th September, 12:30-14:00Women’s LunchVice Chancellors Dining Room, McKinnon Building 67

I Wednesday 28th September, 18:30Conference DinnerLagoon Restaurant, Stuart Park, North Wollongong

Annual General Meeting of the Society

I Wednesday 28th September 2011, 16:00-17:00Hope Theatre

Conference Information Desk

The information desk for the conference is located in the foyer of the Hope Theatre. This desk willbe staffed each day of the conference during the morning.

Book and Software Display

Throughout the conference, Cambridge University Press will be displaying their wares in the foyer ofBuilding 24.

6

Timetable of Events at a Glance

Except for the Welcome cocktails at the Novotel North Beach, North Wollongong and the conferencedinner at the Lagoon Restaurant, Stuart Park, North Wollongong, all main conference events willtake place at the main University of Wollongong campus.Plenary lectures will be in the Hope Theatre and Special Sessions will take place in Building 24.Plenary lectures and keynote talks should finish (including questions) at 55 minutes past their allottedstart time, and contributed talks at 25 minutes past their allotted start time.

Saturday September 24Time Details Location13:00 - 16:00 ECR Workshop Chifley Hotel, Wollongong

Sunday September 25Time Details Location13:00 - 16:00 ECR Workshop Chifley Hotel, Wollongong16:00 - 18:00 Welcome Cocktails Novotel North Beach, North Wollongong

Monday September 26Time Details Location08:30 - 09:30 Registration Hope Theatre09:30 - 11:00 Opening Ceremony and Welcome Hope Theatre11:00 - 11:30 Morning Tea Hope Theatre Foyer11:30 - 12:30 Plenary talk: Nalini Joshi Hope Theatre12:30 - 13:45 Lunch12:30 - 13:45 ECR Lunch SMART Building 6.10513:45 - 14:00 AMSI Intern Program Hope Theatre14:00 - 15:00 Plenary talk: Paul Tod Hope Theatre15:00 - 17:30 Special Sessions

Tuesday September 27Time Details Location09:00 - 10:00 Plenary talk: John Sader Hope Theatre10:00 - 10:30 Morning Tea Hope Theatre Foyer10:30 - 12:30 Special Sessions12:30 - 14:00 Lunch12:30 - 14:00 Womens Lunch Vice Chancellors Dining Room, McKinnon

Building 6714:00 - 15:00 Plenary talk: Vigleik Angeltveit Hope Theatre15:00 - 17:00 Special Sessions15:00 - 18:30 Education Afternoon and Reception Hope Theatre18:30 Public Lecture: Mick Roberts Hope Theatre

7

Timetable of Events at a Glance

Wednesday September 28Time Details Location09:00 - 10:00 Plenary talk: George Willis Hope Theatre10:00 - 11:00 ARC Presentation: Leanne Harvey Hope Theatre11:00 - 11:30 Morning Tea Hope Theatre Foyer11:30 - 13:00 Special Sessions13:00 - 14:00 Lunch14:00 - 15:00 Plenary talk: Hiroshi Matano Hope Theatre15:00 - 15:30 Afternoon Tea Hope Theatre Foyer15:30 - 16:00 NCMS talk: Nalini Joshi Hope Theatre16:00 - 17:00 Annual General Meeting Hope Theatre18:30 Conference Dinner Lagoon Restaurant

Thursday September 29Time Details Location09:00 - 10:00 Plenary talk: Mick Roberts Hope Theatre10:00 - 10:30 Morning Tea Hope Theatre Foyer10:30 - 12:30 Special Sessions Hope Theatre12:30 - 14:00 Lunch

Thursday September 29 and Friday September 30ALTC-AustMS Professional Development Workshop 2011: Effective Teaching, Effective Learning inthe Quantitative Disciplines

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Plenary Lectures and Public Lecture

B Mon 26 September 2011 – Hope Theatre

11:30 I Nalini Joshi (University of Sydney)

Geometric Asymptotics or “How I learnt to stop worrying and love exceptional Lie groups”

14:00 I Kenneth Paul Tod (University of Oxford)

Penrose’s Weyl Curvature Hypothesis and his Conformal Cyclic Cosmology

B Tuesday 27 September 2011 – Hope Theatre

09:00 I John Sader (The University of Melbourne)

How mathematics can help to measure atomic scale phenomena, design spacecraft andpredict the flow of ornate water fountains

14:00 I Vigleik Angeltveit (Australian National University)

Algebraic K-theory via the trace method

18:30 I Mick Roberts (Massey University)

Public Lecture: The mathematics of epidemics and pandemics

B Wednesday 28 September 2011 – Hope Theatre

09:00 I George Willis (The University of Newcastle)

Totally disconnected, locally compact groups

14:00 I Hiroshi Matano (University of Tokyo)

Traveling waves in a sawtoothed cylinder and their homogenization limit

B Thursday 29 September 2011 – Hope Theatre


Mathematical models for the evolution and transmission of a virus

9

Special Session 1: Algebra and Number Theory

Organisers James Parkinson, Anne Thomas

Keynote Talk

B Mon 26 September 2011 – 21.104

15:00 Wadim Zudilin (The University of Newcastle)Ramanujan-style mathematics for Mahler measures

Contributed Talks


16:00 James Wan (University of Newcastle)Legendre Polynomials and Ramanujan-like series for 1/π

16:30 Justin Koonin (University of Sydney)Toplogy of eigenspace posets for unitary reflection groups

17:00 Joanne Hall (Royal Melbourne Institute of Technology)Structure of Hjelmslev planes over Galois rings.

B Tuesday 27 September 2011 – 21.104

10:30 Martin Bunder (University of Wollongong)Lucas Functions and Sums of Powers of Irrationals

11:00 Andrew Crisp (University of Sydney)An exotic Springer correspondence

11:30 Omar Ortiz (The University of Melbourne)Homogeneous Spaces of p-Compact Groups

12:00 Daniel Horadam (University of Newcastle)Fractal Groups and Automata

15:00 Ville Merila (University of Newcastle)Diophantine approximation of q-continued fractions

15:30 Sangeeta Jhanjee (Monash University)Various generalisations of minimax theorem using Clifford algebras

16:00 Alex Ghitza (The University of Melbourne)Lifting modular forms

16:30 Jie Du (University of New South Wales)Representations of Affine q-Schur Algebras

17:00 Wilson Ong (Australian National University)An Alternative Proof of Hesselholt’s Conjecture on Galois Cohomology of WittVectors of Algebraic Integers

B Wednesday 28 September 2011 – 21.104

11:30 James Parkinson (University of Sydney)A complete classification of commutative parabolic Hecke algebras

12:00 Michael Giudici (The University Of Western Australia)Generalised quadrangles with a group acting primitively on points and lines

12:30 Murray Elder (The University of Newcastle)New results about Baumslag-Solitar groups

10

2. Algebra and Number Theory

B Thursday 29 September 2011 – 21.104

10:30 Attila Egri-Nagy (University of Western Sydney)Dependency Functions in Hierarchical (De)Compositions of Finite TransformationSemigroups

11:00 James East (University of Western Sydney)Defining relations for idempotent generators in finite semigroups of mappings

11:30 Anthony Henderson (University of Sydney)Small representations and the affine Grassmannian

12:00 Nora Ganter (The University of Melbourne)Characters of categorical representations

12:30 Debargha Banerjee (Australian National University)Endomorphism algebras of modular motives

11

Special Session 2: Calculus of Variations and PartialDifferential Equations

Organisers Ben Andrews, Yihong Du

Contributed Talks


15:00 Alan McIntosh (Australian National University)Finite Speed of Propagation for First Order Systems and Second Order Operators

15:30 Julie Clutterbuck (Australian National University)Optimal bounds for the first Neumann eigenvalue on a manifold

16:00 Paul Bryan (Australian National University)Isoperimetric comparison techniques for Ricci flow on surfaces and curve shorteningflow

16:30 Menaka Lashitha Bandara (Australian National University)The Kato square root problem on vector bundles of generalised bounded geometry

17:00 Stephen Michael McCormick (Monash University)Dain’s variational principle and its relation to an angular momentum-mass inequalityin general relativity


10:30 Parinya Sa Ngiamsunthorn (University of Sydney)Persistence of bounded solutions of parabolic equations under domain perturbation

11:00 David Hartley (Monash University)Study of Mean Curvature Flow Equations using Functional Analysis

11:30 Lin-Feng Mei (University of New England)On a nonlocal equation modelling phytoplankton growth

12:00 Sanjiban Santra (University of Sydney)Asymptotic behavior of the least energy solution of a problem with competing powers

15:00 Joseph Grotowski (The University of Queensland)New Boundary Regularity Results for Elliptic Systems.

15:30 Todd Oliynyk (Monash University)There are no magnetically charged particle-like solutions of the Einstein-Yang-Millsequations for models with Abelian residual groups

16:00 Frederic Rochon (Australian National University)Asymptotics of complete Kahler metrics of finite volume on quasiprojective manifolds

16:30 Nicholas Fewster-Young (University of New South Wales)Existence of solutions to second order nonlinear singular boundary value problems.


11:30 Xu-Jia Wang (Australian National University)Regularity of elliptic and parabolic equation along a vector field

12:00 Daniel Daners (University of Sydney)An isoperimetric inequality related to a Bernoulli problem

12:30 Florica Cirstea (University of Sydney)On the classification of isolated singularities for nonlinear elliptic equations

12

3. Calculus of Variations and Partial Differential Equations


10:30 Yihong Du (University of New England)Propagation in a time-periodic nonlinear diffusion problem with free boundary

11:00 James McCoy (University of Wollongong)Fully nonlinear curvature flow with nonconvex initial data

11:30 Edward Norman Dancer (University of Sydney)Large interaction problems for non-linear P.D.E.

13

Special Session 3: Computational Mathematics

Organiser Bishnu Prasad Lamichhane

Keynote Talk

B Tuesday 27 September 2011 – 24.G01

11:30 Jonathan Borwein (The University of Newcastle)Mahler measures, short walks and log-sine integrals: A case study in hybridcomputation

Contributed Talks

B Mon 26 September 2011 – 24.G01

15:00 Bishnu Lamichhane (University of Newcastle)A Stabilized Mixed Finite Element Method for the Biharmonic Equation Based onBiorthogonal Systems

15:30 Qinian Jin (Australian National University)Inexact Newton regularization methods

16:00 Quoc Thong Le Gia (University of New South Wales)Solving parabolic equations on the unit sphere via Laplace transforms

16:30 Sudi Mungkasi (Australian National University)Approximations of the Carrier-Greenspan periodic solution to the shallow water waveequations for flows on a sloping beach


10:30 Vivien Challis (University of Queensland)Implementing a topology optimisation algorithm on the GPU

11:00 Stuart Hawkins (Macquarie University)A fully discrete Galerkin algorithm for high frequency exterior acoustic scattering inthree dimensions

15:00 Petrus H Potgieter (University of South Africa)On the fixed points of computable functions

15:30 Paul Leopardi (Australian National University)Can compatible discretization, finite element methods, and discrete Clifford analysisbe fruitfully combined?

14

Special Session 4: Aspects of Applications inMathematics

Organisers Barry Cox, Georg Gottwald

Contributed Talks


15:00 Christopher Angstmann (University of New South Wales)Turing patterns and subcellular protein localisation

15:30 Andrew Francis (University of Western Sydney)The acquisition of genetic pathways in bacteria

16:00 Peter Kim (University of Sydney)Role of regulatory T cells in producing a robust immune response and maintainingimmunodominance

16:30 Graeme Pettet (Queensland University of Technology)In silico investigation of clonal dynamics in the epidermis: simulating the SingleProgenitor Cell model.

17:00 Martin Wechselberger (University of Sydney)Understanding Anomalous Delays in Models of Intracellular Calcium Dynamics


15:00 Tonghua Zhang (Swinburne University of Technology)Stability and bifurcation analysis of a mathematical model for gene expression

15:30 Alla Shymanska (Auckland University of Technology)Mathematical modelling of image converters and intensifiers

16:00 Philip Howes (University of Sydney)Painleve II Asymptotics

16:30 Samuel Butler (University of Sydney)Multidimensional Discrete Inverse Scattering

17:00 Robyn Stuart (University of New South Wales)Almost-invariant sets in open dynamical systems


10:30 Jim Denier (University of Adelaide)Finite-time singularities in the boundary-layer equations: the fluid filled torus

11:30 Dimetre Triadis (La Trobe University)Infiltration in the Green-Ampt limit.

12:00 Joel Moitsheki (University of the Witwatersrand)Transient heat transfer in longitudinal fins of various profiles withtemperature-dependent thermal conductivity and heat transfer coefficient

15:00 Bruce Henry (University of New South Wales)Fokker-Planck equations for anomalous subdiffusion in space-and-time-dependentforce fields

15:30 Govind Menon (Brown University)How long does it take to compute the eigenvalues of a random matrix

16:00 Ben Goldys (University of New South Wales)Liouville theorem for some infinite-dimensional diffusions

15

5. Aspects of Applications in Mathematics

16:30 Tony Roberts (University of Adelaide)Stochastic self-similar solutions emerge from stochastic reaction-diffusion equation

B Wednesday 28 September 2011 – 24.G02

11:30 Thien Tran-Duc (University of Wollongong)General Model for Molecular Interactions in a Benzene Dimer

12:00 Ngamta Thamwattana (University of Wollongong)Modeling encapsulation of acetylene molecules into carbon nanotubes

12:30 Barry Cox (University of Adelaide)Model for carbon nanocones

B Thursday 29 September 2011 – 24.G02

10:30 Robert Marangell (University of Sydney)Stability and Instability in Kink-wave Solutions to the Sine-Gordon Equation

11:00 Thi Dinh Tran (University of New South Wales)Complete integrability of mappings obtained from the discrete Kortegweg-De Vriesand a double copy of the discrete potential Kortegweg-De Vries equations

11:30 James Atkinson (University of Sydney)On exact solutions of integrable discrete equations

12:00 Nalini Joshi (University of Sydney)The repellor and the limit set in complex dynamics of the Painleve equations

16

Special Session 5: Operator Algebras andNoncommutative Geometry

Organisers Nathan Brownlowe, Denis Potapov

Keynote Talk


10:30 Alexander Kumjian (University of Wollongong)Cohomology of higher rank graphs

Contributed Talks


11:30 Nathan Brownlowe (University of Wollongong)On some simple and purely infinite Exel-Larsen crossed product C∗-algebras

12:00 Hui Li (University of Wollongong)A new perspective on topological graph algebras

15:00 Ben Maloney (University of Wollongong)Actions of Ore Semigroups on Higher Rank graphs

15:30 Michael Whittaker (University of Wollongong)Spectral Triples for Hyperbolic Dynamical Systems

16:00 Adam Rennie (Australian National University)Dimension in noncommutative geometry

16:30 Snigdhayan Mahanta (The University of Adelaide)Twisted K-theory and bivariant Chern–Connes type character of some infinitedimensional spaces


10:30 Aidan Sims (University of Wollongong)Equivalence and amenability for Fell bundles

11:00 Valentin Deaconu (University of Nevada, Reno)Entropy of shifts on topological graph C∗-algebras

11:30 Samuel Webster (University of Wollongong)k-coloured graphs and k-graphs.

12:00 Sooran Kang (University of Wollongong)Co-universal C∗-algebras associated with aperiodic k-graphs

17

Special Session 6: Optimisation

Organisers Natashia Boland, Andrew Eberhard

Keynote Talk


10:30 Matthias Ehrgott (The Univesrity of Auckland)Duality and Algorithms for Multiobjective Linear Programming

Contributed Talks


11:30 Peter Malkin (BHP Billiton)Sherali-Adams Relaxations of Graph Isomorphism Polytopes

12:00 Natashia Boland (The University of Newcastle)Lagrangian decomposition: a hierarchy of decompositions and computationaltrade-offs

15:00 Andrew Craig Eberhard (Royal Melbourne Institute of Technology)Some Algorithms in Revealed Preference Theory

15:30 Brailey Sims (University of Newcastle)Alternating projection type algorithms in the absence of convexity

16:00 Faramroze Engineer (University of Newcastle)Turbo-charging the Feasibility Pump

16:30 Francisco Javier Aragon Artacho (The University of Newcastle)Lipschitzian properties of Newton’s iteration


10:30 Boris Miller (Monash University)Optimization of connected controlled Markov chains

11:00 Masoud Talebian (University of Newcastle)Dynamic Assortment and Pricing under Demand Learning

11:30 Jerzy Filar (Flinders University)Identifying non-Hamiltonicity of cubic graphs by nested linear programming

12:00 Christopher John Price (University of Canterbury)Recycling bases in the Halton sequence: an optimization view

18

Special Session 7: Geometry and Topology

Organisers Finnur Larusson, Craig Westerland

Keynote Talk


15:00 Vigleik Angeltveit (Australian National University)Uniqueness of Morava K-theory.

Contributed Talks


16:00 Anne Thomas (University of Sydney)Finite and infinite generation of lattices on right-angled buildings

16:30 Bryan Wang (Australian National University)Stringy product on orbifold K-theory


10:30 Henry Segerman (The University of Melbourne)Triangulations of hyperbolic 3-manifolds admitting strict angle structures

11:00 Norman Do (The University of Melbourne)Counting lattice points in compactified moduli spaces of curves

11:30 Tyson Ritter (University of Adelaide)Acyclic Embeddings of Open Riemann Surfaces into Elliptic Manifolds

12:00 Tharatorn Supasiti (The University of Melbourne)On JSJ decomposition theorem for Haken 3-manifolds

15:00 Snigdhayan Mahanta (The University of Adelaide)Assembly maps and the integral K-theoretic Novikov conjecture

15:30 Elizabeth Stanhope (Lewis and Clark College/The University of Melbourne)Controlling orbifold topology via the Laplace spectrum

16:00 Alexander Hanysz (University of Adelaide)Oka properties of some hypersurface complements

16:30 Ali Sayed Elfard (University of Wollongong)On free paratopological groups

B Wednesday 28 September 2011 – 24.G03

11:30 Facundo Memoli (University of Adelaide)Stability of Persistent Homology Invariants

12:00 Volker Gebhardt (University of Western Sydney)Finite index subgroups of mapping class groups

12:30 Craig Westerland (The University of Melbourne)Twisted Morava K-theory

B Thursday 29 September 2011 – 24.G03

10:30 Michael Eastwood (Australian National University)Some remarks on linear elasticity

11:00 Finnur Larusson (University of Adelaide)Deformations of Oka manifolds

19

8. Geometry and Topology

11:30 Nora Ganter (The University of Melbourne)Topological K-theory

12:00 Laurentiu Paunescu (University of Sydney)A’Campo curvature bumps

20

Special Session 8: Topological Groups and HarmonicAnalysis

Organiser George Willis

Keynote Talk


10:30 Hung Le Pham (Victoria University of Wellington)Multi-norms and amenability of groups

Contributed Talks


11:30 Michael Cowling (University of New South Wales)The Fourier-Stieltjes algebra and group geometry

12:00 Andrew Morris (University of Newcastle)Quaternic Wavelets


11:30 Xuan Duong (Macquarie University)Boundedness of singular integrals and their commutators with BMO functions onHardy spaces.

12:00 Jeffrey Hogan (University of Newcastle)Higher-dimensional Clifford Fourier transforms

12:30 George Willis (The University of Newcastle)Weighted convolution algebras on locally compact groups

21

Special Session 9: Financial Mathematics

Organisers Fima Klebaner, Song Ping Zhu

Keynote Talk


10:30 Carl Chiarella (University of Technology, Sydney)Pricing Interest Rate Derivatives in a Multifactor HJM Model with Time DependentVolatility

Contributed Talks


11:30 Song-Ping Zhu (University of Wollongong)Analytically pricing Parisian and Parasian options

12:00 Kais Hamza (Monash University)Martingales with given marginals

15:00 Guanghua Lian (Auckland University of Technology)Consistent Modeling of SPX and VIX Options: Efficient Evaluation Issues inGatheral’s Three-factor Model

15:30 Ivan Guo (University of Sydney)Multi-Player Dynkin Games

16:00 Marianito Rodrigo (University of Wollongong)Calibration of Vasicek and CIR interest rate models via generating functions

16:30 Joanna Goard (University of Wollongong)Pricing of volatility derivatives using 3/2 stochastic models

22

Special Session 10: Combinatorics

Organiser Alice Devillers

Keynote Talk


15:00 Dillon Mayhew (Victoria University of Wellington)Recent research in matroid theory

Contributed Talks


16:00 Neil Gillespie (The University Of Western Australia)Characterising a family of Neighbour Transitive Codes

16:30 Bao Ho (La Trobe University)The Sprague-Grundy function for the real game Euclid


15:00 Cheryl Praeger (The University Of Western Australia)Normal coverings of finite symmetric and alternating groups

15:30 Alice Devillers (The University Of Western Australia)On quasiprimitive rank 3 permutation groups

16:00 Akos Seress (The University Of Western Australia)Disconnected colors in generalized Gallai colorings


11:30 Jennifer Seberry (University of Wollongong)Higher dimensional Hadamard matrices

12:00 Barbara Maenhaut (The University of Queensland)Almost regular edge colourings of complete bipartite graphs

12:30 Richard P Brent (Australian National University)Computing Bernoulli and Tangent numbers

23

Special Session 11: Probability and Statistics

Organiser Mark Fielding

Contributed Talks


15:00 Andriy Olenko (La Trobe University)Abelian and Tauberian theorems for long memory random fields

15:30 Michaael McCrae (AMSI)Statistical Based Arbitrage in Financial Markets using Cointegration

16:00 You-Gan Wang (University of Queensland)Gaussian Working Correlation Structure in Longitudinal Data Analysis

16:30 Shuangzhe Liu (AMSI)Influence diagnostics for INGARCH time series models


11:30 Mark James Fielding (University of Wollongong)Gaussian processes in Hybrid MCMC and Simulated Annealing for computationallyexpensive objective functions.

12:00 Scott Sisson (AMSI)Approximate Bayesian computation (ABC) and Bayes linear analysis: Towardshigh-dimensional ABC

12:30 John Ormerod (University of Sydney)Hybrid Variational Bayes

24

Special Session 12: General session

Organiser Aidan Sims

Contributed Talks


15:00 Ian Doust (University of New South Wales)Metric trees of generalized roundness one

15:30 Stephen James Sanchez (University of New South Wales)p-negative type of finite metric spaces

16:00 Nicholas Bartlett (AMSI)Hall-Littlewood polynomials and generalisations of the Rogers–Ramanujan identities.

16:30 Vladimir Gaitsgory (University of South Australia)Singularly Perturbed Linear Programming Problems


10:30 Raymond Booth (Flinders University)The Vanishing Art of Introductory Mathematics

11:00 Prabhu Manyem (Shanghai University)Nearly Identical Expressions in Existential Second Order Logic for Problems in P andNP

11:30 Rupert Gordon McCallum (University of New South Wales)A new large cardinal property

25

Special Session 13: Mathematical Physics

Organiser Gavin Brennen

Contributed Talks


15:00 Ian Marquette (The University of Queensland)Polynomial algebras and superintegrability

15:30 Amir Moghaddam (The University of Queensland)Integrable Quantum Impurity Models

16:00 Andrew Birrell (University of Queensland)Integrability of BEC/BCS crossover Hamiltonians

16:30 Caley Finn (The University of Melbourne)Dynamics of the asymmetric exclusion process in the reverse bias regime

17:00 Jan De Gier (The University of Melbourne)Current fluctuations in the asymmetric exclusion process


10:30 Eduardo Cerutti Mattei (The University of Queensland)Integrable Heteroatomic Molecular Bose-Einstein Condensates

11:00 Frank De Silva (AMSI/University of Melbourne)The simplest correction to Hubbell’s law and its theoretical implications

11:30 Maria Tsarenko (The University of Melbourne)Random Tilings of Squares Triangles and Rhombi

12:00 Alex Lee (The University of Melbourne)Matrix models, lattice models and an O(N)-Potts correspondence


11:30 Timothy Garoni (Monash University)Loop models in three dimensions

12:00 Nicholas Beaton (MASCOS / University of Melbourne)A non-directed model of polymer adsorption

12:30 Anthony Mays (The University of Melbourne)A geometric triumvirate of random matrices


10:30 Demosthenes Ellinas (Technical University of Crete)Quantum Master Equations from Operator Valued Measures: A Hopf AlgebraicApproach

11:00 Peter Forrester (The University of Melbourne)A Fuchsian differential equation for Selberg correlation integrals

11:30 Andrea Bedini (MASCOS / University of Melbourne)From second-order to first-order in an infinite number of steps

12:00 Andrew Norton (Max Planck Institute for Gravitational Physics)The equation of motion of an extended charged particle

26

Special Session 14: Differential Geometry

Organiser Michael Eastwood

Keynote Talk


15:00 Rod Gover (AMSI)Families of conformal operators along a hypersurface and formal extension problems

Contributed Talks


16:00 Matthew Randall (Australian National University)Local obstructions to 2-dimensional projective structures admitting skew-symmetricRicci tensor

16:30 Ana Hinic-Galic (La Trobe University)Totally geodesic subalgebras of N-graded filiform Lie algebras


10:30 Arman Taghavi-Chabert (Masaryk University)Twistor geometry in six dimensions

11:00 Thomas Leistner (University of Adelaide)Connected irreducible subgroups of O(2, n)

11:30 Andreas Cap (University of Vienna)Infinitesimal automorphisms of parabolic geometries and dynamics

12:00 Michael Fielding Barnsley (Australian National University)Fractal transformations associated with Bernoulli convolutions

15:30 Vladimir Soucek (Charles University)Dunkl operators and a family of realizations of osp(1|2)

16:00 Mathew Langford (Australian National University)Asymptotic Convexity of Hypersurfaces Moving by Curvature

16:30 Naghmana Tehseen (La Trobe University)Geometric approach to partial differential equations


11:30 Katharina Neusser (Australian National University)On some generic distributions and their automorphism groups

12:00 Dennis The (Australian National University)Rigidity of Schubert varieties in compact Hermitian symmetric spaces

12:30 Katja Sagerschnig (Australian National University)(2, 3, 5)-distributions and associated conformal structures


11:30 Tohru Morimoto (Kinki University)Subriemannian curvatures

12:00 Petr Somberg (Charles University)Howe duality for the symplectic Dirac operator

27

Special Session 15: Education Afternoon

Organiser Jacqui Ramagge, Caz Sanderson

B Tuesday 27 September 2011 – Hope Theatre

15:00 Registration (Hope Theatre Foyer)

Invited Talks15:30 Michael Giudici (University of Western Australia)

Wallpaper, Crystals and Symmetry

16:00 Michael Barnsley (Australian National University)Fractals and Dynamics in Education

16:30 Panel Discussion: Cave or Tunnel? Is there light ahead? (Hope Theatre)Dean Jones (Head of Mathematics, Smiths High HS)Nalini Joshi (Chair of Australian Academy of Science, National Committee ofMathematical Sciences)Janine McIntosh (AMSI)Jacqui Ramagge (University of Wollongong)

Education Afternoon Reception 17:30 – 18:30

Public Lecture18:30 Mick Roberts (Massey University)

The mathematics of epidemics and pandemics

28

Conference TimetableMon 26 September 2011

Registration – Hope Theatre 08:30 – 09:30

Welcome Ceremony – Hope Theatre 09:30 – 11:00

Morning Tea – Hope Theatre Foyer 11:00 – 11:30

Plenary Lecture – Hope Theatre

11:30 I Nalini Joshi (University of Sydney)

Geometric Asymptotics or “How I learnt to stop worrying and love exceptional Lie groups”

Lunch 12:30 – 13:45

AMSI Intern Programme Information – Hope Theatre 13:45 – 14:00


14:00 I Kenneth Paul Tod (University of Oxford)

Penrose’s Weyl Curvature Hypothesis and his Conformal Cyclic Cosmology

Afternoon Special SessionsStart 15:00 15:30 16:00 16:30 17:00

24.104 1: Zudilin 1: Wan 1: Koonin 1: Hall24.103 2: McIntosh 2: Clutterbuck 2: Bryan 2: Bandara 2: McCormick

24.G01 3: Lamichhane 3: Jin 3: Le Gia 3: Mungkasi24.G02 4: Angstmann 4: Francis 4: Kim 4: Pettet 4: Wechselberger24.105 4: Zhang 4: Shymanska 4: Howes 4: Butler 4: Stuart

24.G03 7: Angeltveit 7: Thomas 7: Wang24.201 10: Mayhew 10: Gillespie 10: Ho24.101 11: Olenko 11: McCrae 11: Wang 11: Liu24.202 13: Marquette 13: Moghaddam 13: Birrell 13: Finn 13: De Gier24.203 14: Gover 14: Randall 14: Hinic-Galic


24.104

15:00 Wadim Zudilin (The University of Newcastle)Ramanujan-style mathematics for Mahler measures

16:00 James Wan (University of Newcastle)Legendre Polynomials and Ramanujan-like series for 1/π

16:30 Justin Koonin (University of Sydney)Toplogy of eigenspace posets for unitary reflection groups

17:00 Joanne Hall (Royal Melbourne Institute of Technology)Structure of Hjelmslev planes over Galois rings.

29

Mon 26 September 2011


24.103

15:00 Alan McIntosh (Australian National University)Finite Speed of Propagation for First Order Systems and Second Order Operators

15:30 Julie Clutterbuck (Australian National University)Optimal bounds for the first Neumann eigenvalue on a manifold

16:00 Paul Bryan (Australian National University)Isoperimetric comparison techniques for Ricci flow on surfaces and curve shorteningflow

16:30 Menaka Lashitha Bandara (Australian National University)The Kato square root problem on vector bundles of generalised bounded geometry

17:00 Stephen Michael McCormick (Monash University)Dain’s variational principle and its relation to an angular momentum-mass inequalityin general relativity

3. Computational Mathematics

24.G01

15:00 Bishnu Lamichhane (University of Newcastle)A Stabilized Mixed Finite Element Method for the Biharmonic Equation Based onBiorthogonal Systems

15:30 Qinian Jin (Australian National University)Inexact Newton regularization methods

16:00 Quoc Thong Le Gia (University of New South Wales)Solving parabolic equations on the unit sphere via Laplace transforms

16:30 Sudi Mungkasi (Australian National University)Approximations of the Carrier-Greenspan periodic solution to the shallow water waveequations for flows on a sloping beach


24.G02

15:00 Christopher Angstmann (University of New South Wales)Turing patterns and subcellular protein localisation

24.105

15:00 Tonghua Zhang (Swinburne University of Technology)Stability and bifurcation analysis of a mathematical model for gene expression

24.G02

15:30 Andrew Francis (University of Western Sydney)The acquisition of genetic pathways in bacteria

24.105

15:30 Alla Shymanska (Auckland University of Technology)Mathematical modelling of image converters and intensifiers

24.G02

16:00 Peter Kim (University of Sydney)Role of regulatory T cells in producing a robust immune response and maintainingimmunodominance

24.105

16:00 Philip Howes (University of Sydney)Painleve II Asymptotics

24.G02

16:30 Graeme Pettet (Queensland University of Technology)In silico investigation of clonal dynamics in the epidermis: simulating the SingleProgenitor Cell model.

30


24.105

16:30 Samuel Butler (University of Sydney)Multidimensional Discrete Inverse Scattering

24.G02

17:00 Martin Wechselberger (University of Sydney)Understanding Anomalous Delays in Models of Intracellular Calcium Dynamics

24.105

17:00 Robyn Stuart (University of New South Wales)Almost-invariant sets in open dynamical systems


24.G03

15:00 Vigleik Angeltveit (Australian National University)Uniqueness of Morava K-theory.

16:00 Anne Thomas (University of Sydney)Finite and infinite generation of lattices on right-angled buildings

16:30 Bryan Wang (Australian National University)Stringy product on orbifold K-theory

10. Combinatorics

24.201

15:00 Dillon Mayhew (Victoria University of Wellington)Recent research in matroid theory

16:00 Neil Gillespie (The University Of Western Australia)Characterising a family of Neighbour Transitive Codes

16:30 Bao Ho (La Trobe University)The Sprague-Grundy function for the real game Euclid

11. Probability and Statistics

24.101

15:00 Andriy Olenko (La Trobe University)Abelian and Tauberian theorems for long memory random fields

15:30 Michaael McCrae (AMSI)Statistical Based Arbitrage in Financial Markets using Cointegration

16:00 You-Gan Wang (University of Queensland)Gaussian Working Correlation Structure in Longitudinal Data Analysis

16:30 Shuangzhe Liu (AMSI)Influence diagnostics for INGARCH time series models

13. Mathematical Physics

24.202

15:00 Ian Marquette (The University of Queensland)Polynomial algebras and superintegrability

15:30 Amir Moghaddam (The University of Queensland)Integrable Quantum Impurity Models

16:00 Andrew Birrell (University of Queensland)Integrability of BEC/BCS crossover Hamiltonians

16:30 Caley Finn (The University of Melbourne)Dynamics of the asymmetric exclusion process in the reverse bias regime

17:00 Jan De Gier (The University of Melbourne)Current fluctuations in the asymmetric exclusion process

31


14. Differential Geometry

24.203

15:00 Rod Gover (AMSI)Families of conformal operators along a hypersurface and formal extension problems

16:00 Matthew Randall (Australian National University)Local obstructions to 2-dimensional projective structures admitting skew-symmetricRicci tensor

16:30 Ana Hinic-Galic (La Trobe University)Totally geodesic subalgebras of N-graded filiform Lie algebras

32

Tuesday 27 September 2011


09:00 I John Sader (The University of Melbourne)

How mathematics can help to measure atomic scale phenomena, design spacecraft andpredict the flow of ornate water fountains


Morning Special SessionsStart 10:30 11:00 11:30 12:00

24.104 1: Bunder 1: Crisp 1: Ortiz 1: Horadam24.103 2: Sa Ngiamsunthorn 2: Hartley 2: Mei 2: Santra

24.G01 3: Challis 3: Hawkins 3: Borwein24.G02 4: Denier 4: Triadis 4: Moitsheki24.101 5: Kumjian 5: Brownlowe 5: Li24.102 6: Ehrgott 6: Malkin 6: Boland

24.G03 7: Segerman 7: Do 7: Ritter 7: Supasiti24.204 8: Pham 8: Cowling 8: Morris24.105 9: Chiarella 9: Zhu 9: Hamza24.202 13: Mattei 13: De Silva 13: Tsarenko 13: Lee24.203 14: Taghavi-Chabert 14: Leistner 14: Cap 14: Barnsley


24.104

10:30 Martin Bunder (University of Wollongong)Lucas Functions and Sums of Powers of Irrationals

11:00 Andrew Crisp (University of Sydney)An exotic Springer correspondence

11:30 Omar Ortiz (The University of Melbourne)Homogeneous Spaces of p-Compact Groups

12:00 Daniel Horadam (University of Newcastle)Fractal Groups and Automata


24.103

10:30 Parinya Sa Ngiamsunthorn (University of Sydney)Persistence of bounded solutions of parabolic equations under domain perturbation

11:00 David Hartley (Monash University)Study of Mean Curvature Flow Equations using Functional Analysis

11:30 Lin-Feng Mei (University of New England)On a nonlocal equation modelling phytoplankton growth

12:00 Sanjiban Santra (University of Sydney)Asymptotic behavior of the least energy solution of a problem with competing powers

33



24.G01

10:30 Vivien Challis (University of Queensland)Implementing a topology optimisation algorithm on the GPU

11:00 Stuart Hawkins (Macquarie University)A fully discrete Galerkin algorithm for high frequency exterior acoustic scattering inthree dimensions

11:30 Jonathan Borwein (The University of Newcastle)Measures, Walks and Integrals


24.G02

10:30 Jim Denier (University of Adelaide)Finite-time singularities in the boundary-layer equations: the fluid filled torus

11:30 Dimetre Triadis (La Trobe University)Infiltration in the Green-Ampt limit.

12:00 Joel Moitsheki (University of the Witwatersrand)Transient heat transfer in longitudinal fins of various profiles withtemperature-dependent thermal conductivity and heat transfer coefficient

5. Operator Algebras and Noncommutative Geometry

24.101

10:30 Alexander Kumjian (University of Wollongong)Cohomology of higher rank graphs

11:30 Nathan Brownlowe (University of Wollongong)On some simple and purely infinite Exel-Larsen crossed product C∗-algebras

12:00 Hui Li (University of Wollongong)A new perspective on topological graph algebras

6. Optimisation

24.102

10:30 Matthias Ehrgott (The Univesrity of Auckland)Duality and Algorithms for Multiobjective Linear Programming

11:30 Peter Malkin (BHP Billiton)Sherali-Adams Relaxations of Graph Isomorphism Polytopes

12:00 Natashia Boland (The University of Newcastle)Lagrangian decomposition: a hierarchy of decompositions and computationaltrade-offs


24.G03

10:30 Henry Segerman (The University of Melbourne)Triangulations of hyperbolic 3-manifolds admitting strict angle structures

11:00 Norman Do (The University of Melbourne)Counting lattice points in compactified moduli spaces of curves

11:30 Tyson Ritter (University of Adelaide)Acyclic Embeddings of Open Riemann Surfaces into Elliptic Manifolds

12:00 Tharatorn Supasiti (The University of Melbourne)On JSJ decomposition theorem for Haken 3-manifolds

34


8. Topological Groups and Harmonic Analysis

24.204

10:30 Hung Le Pham (Victoria University of Wellington)Multi-norms and amenability of groups

11:30 Michael Cowling (University of New South Wales)The Fourier-Stieltjes algebra and group geometry

12:00 Andrew Morris (University of Newcastle)Quaternic Wavelets

9. Financial Mathematics

24.105

10:30 Carl Chiarella (University of Technology, Sydney)Pricing Interest Rate Derivatives in a Multifactor HJM Model with Time DependentVolatility

11:30 Song-Ping Zhu (University of Wollongong)Analytically pricing Parisian and Parasian options

12:00 Kais Hamza (Monash University)Martingales with given marginals


24.202

10:30 Eduardo Cerutti Mattei (The University of Queensland)Integrable Heteroatomic Molecular Bose-Einstein Condensates

11:00 Frank De Silva (AMSI/University of Melbourne)The simplest correction to Hubbell’s law and its theoretical implications

11:30 Maria Tsarenko (The University of Melbourne)Random Tilings of Squares Triangles and Rhombi

12:00 Alex Lee (The University of Melbourne)Matrix models, lattice models and an O(N)-Potts correspondence


24.203

10:30 Arman Taghavi-Chabert (Masaryk University)Twistor geometry in six dimensions

11:00 Thomas Leistner (University of Adelaide)Connected irreducible subgroups of O(2, n)

11:30 Andreas Cap (University of Vienna)Infinitesimal automorphisms of parabolic geometries and dynamics

12:00 Michael Fielding Barnsley (Australian National University)Fractal transformations associated with Bernoulli convolutions

Lunch 12:30 – 14:00


14:00 I Vigleik Angeltveit (Australian National University)

Algebraic K-theory via the trace method

35


Afternoon Special SessionsStart 15:00 15:30 16:00 16:30 17:00

24.104 1: Merila 1: Jhanjee 1: Ghitza 1: Du 1: Ong24.103 2: Grotowski 2: Oliynyk 2: Rochon 2: Fewster-Young

24.G01 3: Potgieter 3: Leopardi24.G02 4: Henry 4: Menon 4: Goldys 4: Roberts24.101 5: Maloney 5: Whittaker 5: Rennie 5: Mahanta24.102 6: Eberhard 6: Sims 6: Engineer 6: Aragn Artacho

24.G03 7: Mahanta 7: Stanhope 7: Hanysz 7: Elfard24.105 9: Lian 9: Guo 9: Rodrigo 9: Goard24.201 10: Praeger 10: Devillers 10: Seress24.204 12: Doust 12: Sanchez 12: Bartlett 12: Gaitsgory24.203 14: Soucek 14: Langford 14: TehseenHope 15: Registration 15: Giudici 15: Barnsley 15: Panel Discussion


24.104

15:00 Ville Merila (University of Newcastle)Diophantine approximation of q-continued fractions

15:30 Sangeeta Jhanjee (Monash University)Various generalisations of minimax theorem using Clifford algebras

16:00 Alex Ghitza (The University of Melbourne)Lifting modular forms

16:30 Jie Du (University of New South Wales)Representations of Affine q-Schur Algebras

17:00 Wilson Ong (Australian National University)An Alternative Proof of Hesselholt’s Conjecture on Galois Cohomology of WittVectors of Algebraic Integers


24.103

15:00 Joseph Grotowski (The University of Queensland)New Boundary Regularity Results for Elliptic Systems.

15:30 Todd Oliynyk (Monash University)There are no magnetically charged particle-like solutions of the Einstein-Yang-Millsequations for models with Abelian residual groups

16:00 Frederic Rochon (Australian National University)Asymptotics of complete Kahler metrics of finite volume on quasiprojective manifolds

16:30 Nicholas Fewster-Young (University of New South Wales)Existence of solutions to second order nonlinear singular boundary value problems.


24.G01

15:00 Petrus H Potgieter (University of South Africa)On the fixed points of computable functions

15:30 Paul Leopardi (Australian National University)Can compatible discretization, finite element methods, and discrete Clifford analysisbe fruitfully combined?


24.G02

15:00 Bruce Henry (University of New South Wales)Fokker-Planck equations for anomalous subdiffusion in space-and-time-dependentforce fields

36


15:30 Govind Menon (Brown University)How long does it take to compute the eigenvalues of a random matrix

16:00 Ben Goldys (University of New South Wales)Liouville theorem for some infinite-dimensional diffusions

16:30 Tony Roberts (University of Adelaide)Stochastic self-similar solutions emerge from stochastic reaction-diffusion equation


24.101

15:00 Ben Maloney (University of Wollongong)Actions of Ore Semigroups on Higher Rank graphs

15:30 Michael Whittaker (University of Wollongong)Spectral Triples for Hyperbolic Dynamical Systems

16:00 Adam Rennie (Australian National University)Dimension in noncommutative geometry

16:30 Snigdhayan Mahanta (The University of Adelaide)Twisted K-theory and bivariant Chern–Connes type character of some infinitedimensional spaces

6. Optimisation

24.102

15:00 Andrew Craig Eberhard (Royal Melbourne Institute of Technology)Some Algorithms in Revealed Preference Theory

15:30 Brailey Sims (University of Newcastle)Alternating projection type algorithms in the absence of convexity

16:00 Faramroze Engineer (University of Newcastle)Turbo-charging the Feasibility Pump

16:30 Francisco Javier Aragon Artacho (The University of Newcastle)Lipschitzian properties of Newton’s iteration


24.G03

15:00 Snigdhayan Mahanta (The University of Adelaide)Assembly maps and the integral K-theoretic Novikov conjecture

15:30 Elizabeth Stanhope (Lewis and Clark College/The University of Melbourne)Controlling orbifold topology via the Laplace spectrum

16:00 Alexander Hanysz (University of Adelaide)Oka properties of some hypersurface complements

16:30 Ali Sayed Elfard (University of Wollongong)On free paratopological groups


24.105

15:00 Guanghua Lian (Auckland University of Technology)Consistent Modeling of SPX and VIX Options: Efficient Evaluation Issues inGatheral’s Three-factor Model

15:30 Ivan Guo (University of Sydney)Multi-Player Dynkin Games

16:00 Marianito Rodrigo (University of Wollongong)Calibration of Vasicek and CIR interest rate models via generating functions

16:30 Joanna Goard (University of Wollongong)Pricing of volatility derivatives using 3/2 stochastic models

37


10. Combinatorics

24.201

15:00 Cheryl Praeger (The University Of Western Australia)Normal coverings of finite symmetric and alternating groups

15:30 Alice Devillers (The University Of Western Australia)On quasiprimitive rank 3 permutation groups

16:00 Akos Seress (The University Of Western Australia)Disconnected colors in generalized Gallai colorings

12. General session

24.204

15:00 Ian Doust (University of New South Wales)Metric trees of generalized roundness one

15:30 Stephen James Sanchez (University of New South Wales)p-negative type of finite metric spaces

16:00 Nicholas Bartlett (AMSI)Hall-Littlewood polynomials and generalisations of the Rogers–Ramanujan identities.

16:30 Vladimir Gaitsgory (University of South Australia)Singularly Perturbed Linear Programming Problems


24.203

15:30 Vladimir Soucek (Charles University)Dunkl operators and a family of realizations of osp(1|2)

16:00 Mathew Langford (Australian National University)Asymptotic Convexity of Hypersurfaces Moving by Curvature

16:30 Naghmana Tehseen (La Trobe University)Geometric approach to partial differential equations

15. Education Afternoon

Hope Theatre

15:30 Michael Giudici (University of Western Australia)Wallpaper, Crystals and Symmetry

16:00 Michael Barnsley (Australian National University)Fractals and Dynamics in Education

16:30 Panel discussion (Various)Cave or Tunnel? Is there light ahead?

38

Wednesday 28 September 2011


09:00 I George Willis (The University of Newcastle)

Totally disconnected, locally compact groups

ARC Presentation – Leanne Harvey 10:00 – 11:00


Morning Special SessionsStart 11:30 12:00 12:30

24.104 1: Parkinson 1: Giudici 1: Elder24.103 2: Wang 2: Daners 2: Cirstea

24.G02 4: Tran-Duc 4: Thamwattana 4: Cox24.G03 7: Memoli 7: Gebhardt 7: Westerland24.204 8: Duong 8: Hogan24.201 10: Seberry 10: Maenhaut 8: Willis24.101 11: Fielding 11: Sisson 11: Ormerod24.202 13: Garoni 13: Beaton 13: Mays24.203 14: Neusser 14: The 14: Sagerschnig


24.104

11:30 James Parkinson (University of Sydney)A complete classification of commutative parabolic Hecke algebras

12:00 Michael Giudici (The University Of Western Australia)Generalised quadrangles with a group acting primitively on points and lines

12:30 Murray Elder (The University of Newcastle)New results about Baumslag-Solitar groups


24.103

11:30 Xu-Jia Wang (Australian National University)Regularity of elliptic and parabolic equation along a vector field

12:00 Daniel Daners (University of Sydney)An isoperimetric inequality related to a Bernoulli problem

12:30 Florica Cirstea (University of Sydney)On the classification of isolated singularities for nonlinear elliptic equations

39



24.G02

11:30 Thien Tran-Duc (University of Wollongong)General Model for Molecular Interactions in a Benzene Dimer

12:00 Ngamta Thamwattana (University of Wollongong)Modeling encapsulation of acetylene molecules into carbon nanotubes

12:30 Barry Cox (University of Adelaide)Model for carbon nanocones


24.G03

11:30 Facundo Memoli (University of Adelaide)Stability of Persistent Homology Invariants

12:00 Volker Gebhardt (University of Western Sydney)Finite index subgroups of mapping class groups

12:30 Craig Westerland (The University of Melbourne)Twisted Morava K-theory


24.204

11:30 Xuan Duong (Macquarie University)Boundedness of singular integrals and their commutators with BMO functions onHardy spaces.

12:00 Jeffrey Hogan (University of Newcastle)Higher-dimensional Clifford Fourier transforms

24.201

12:30 George Willis (The University of Newcastle)Weighted convolution algebras on locally compact groups

10. Combinatorics

24.201

11:30 Jennifer Seberry (University of Wollongong)Higher dimensional Hadamard matrices

12:00 Barbara Maenhaut (The University of Queensland)Almost regular edge colourings of complete bipartite graphs

12:30 Richard P Brent (Australian National University)Computing Bernoulli and Tangent numbers


24.101

11:30 Mark James Fielding (University of Wollongong)Gaussian processes in Hybrid MCMC and Simulated Annealing for computationallyexpensive objective functions.

12:00 Scott Sisson (AMSI)Approximate Bayesian computation (ABC) and Bayes linear analysis: Towardshigh-dimensional ABC

12:30 John Ormerod (University of Sydney)Hybrid Variational Bayes

40



24.202

11:30 Timothy Garoni (Monash University)Loop models in three dimensions

12:00 Nicholas Beaton (MASCOS / University of Melbourne)A non-directed model of polymer adsorption

12:30 Anthony Mays (The University of Melbourne)A geometric triumvirate of random matrices


24.203

11:30 Katharina Neusser (Australian National University)On some generic distributions and their automorphism groups

12:00 Dennis The (Australian National University)Rigidity of Schubert varieties in compact Hermitian symmetric spaces

12:30 Katja Sagerschnig (Australian National University)(2, 3, 5)-distributions and associated conformal structures

Lunch 13:00 – 14:00


14:00 I Hiroshi Matano (University of Tokyo)

Traveling waves in a sawtoothed cylinder and their homogenization limit

Afternoon Tea – Hope Theatre foyer 15:00 – 15:30

NCMS: Nalini Joshi – Hope Theatre 15:30 – 16:00

AGM – Hope Theatre 16:00 – 17:00

41

Thursday 29 September 2011



Mathematical models for the evolution and transmission of a virus


Morning Special SessionsStart 10:30 11:00 11:30 12:00 12:30

24.104 1: Egri-Nagy 1: East 1: Henderson 1: Ganter 1: Banerjee24.103 2: Du 2: McCoy 2: Dancer

24.G02 4: Marangell 4: Tran 4: Atkinson 4: Joshi24.101 5: Sims 5: Deaconu 5: Webster 5: Kang24.102 6: Miller 6: Talebian 6: Filar 6: Price

24.G03 7: Eastwood 7: Larusson 7: Ganter 7: Paunescu24.204 12: Booth 12: Manyem 12: McCallum24.202 13: Ellinas 13: Forrester 13: Bedini 13: Norton24.203 14: Morimoto 14: Somberg


24.104

10:30 Attila Egri-Nagy (University of Western Sydney)Dependency Functions in Hierarchical (De)Compositions of Finite TransformationSemigroups

11:00 James East (University of Western Sydney)Defining relations for idempotent generators in finite semigroups of mappings

11:30 Anthony Henderson (University of Sydney)Small representations and the affine Grassmannian

12:00 Nora Ganter (The University of Melbourne)Characters of categorical representations

12:30 Debargha Banerjee (Australian National University)Endomorphism algebras of modular motives


24.103

10:30 Yihong Du (University of New England)Propagation in a time-periodic nonlinear diffusion problem with free boundary

11:00 James McCoy (University of Wollongong)Fully nonlinear curvature flow with nonconvex initial data

11:30 Edward Norman Dancer (University of Sydney)Large interaction problems for non-linear P.D.E.

42



24.G02

10:30 Robert Marangell (University of Sydney)Stability and Instability in Kink-wave Solutions to the Sine-Gordon Equation

11:00 Thi Dinh Tran (University of New South Wales)Complete integrability of mappings obtained from the discrete Kortegweg-De Vriesand a double copy of the discrete potential Kortegweg-De Vries equations

11:30 James Atkinson (University of Sydney)On exact solutions of integrable discrete equations

12:00 Nalini Joshi (University of Sydney)The repellor and the limit set in complex dynamics of the Painleve equations


24.101

10:30 Aidan Sims (University of Wollongong)Equivalence and amenability for Fell bundles

11:00 Valentin Deaconu (University of Nevada, Reno)Entropy of shifts on topological graph C∗-algebras

11:30 Samuel Webster (University of Wollongong)k-coloured graphs and k-graphs.

12:00 Sooran Kang (University of Wollongong)Co-universal C∗-algebras associated with aperiodic k-graphs

6. Optimisation

24.102

10:30 Boris Miller (Monash University)Optimization of connected controlled Markov chains

11:00 Masoud Talebian (University of Newcastle)Dynamic Assortment and Pricing under Demand Learning

11:30 Jerzy Filar (Flinders University)Identifying non-Hamiltonicity of cubic graphs by nested linear programming

12:00 Christopher John Price (University of Canterbury)Recycling bases in the Halton sequence: an optimization view


24.G03

10:30 Michael Eastwood (Australian National University)Some remarks on linear elasticity

11:00 Finnur Larusson (University of Adelaide)Deformations of Oka manifolds

11:30 Nora Ganter (The University of Melbourne)Topological K-theory

12:00 Laurentiu Paunescu (University of Sydney)A’Campo curvature bumps

12. General session

24.204

10:30 Raymond Booth (Flinders University)The Vanishing Art of Introductory Mathematics

11:00 Prabhu Manyem (Shanghai University)Nearly Identical Expressions in Existential Second Order Logic for Problems in P andNP

11:30 Rupert Gordon McCallum (University of New South Wales)A new large cardinal property

43



24.202

10:30 Demosthenes Ellinas (Technical University of Crete)Quantum Master Equations from Operator Valued Measures: A Hopf AlgebraicApproach

11:00 Peter Forrester (The University of Melbourne)A Fuchsian differential equation for Selberg correlation integrals

11:30 Andrea Bedini (MASCOS / University of Melbourne)From second-order to first-order in an infinite number of steps

12:00 Andrew Norton (Max Planck Institute for Gravitational Physics)The equation of motion of an extended charged particle


24.203

11:30 Tohru Morimoto (Kinki University)Subriemannian curvatures

12:00 Petr Somberg (Charles University)Howe duality for the symplectic Dirac operator

Lunch 12:30 – 14:00

44

List of Registrants

As of 13 September 2011

Ms Natalie Aisbett University of SydneyDr Vigleik Angeltveit Australian National UniversityDr Christopher Angstmann University of New South WalesDr Francisco Javier Aragon Artacho The University of NewcastleDr James Atkinson University of SydneyMr Alexander Badran University of Technology, SydneyMs Fran Baker The University of NewcastleMr Menaka Lashitha Bandara Australian National UniversityDr Debargha Banerjee Australian National UniversityMr Christopher Banks The University of NewcastleDr Ewan Barker University of BallaratProf Michael Fielding Barnsley Australian National UniversityMr Nicholas Bartlett AMSIProf Andrew Bassom The University Of Western AustraliaMr Nicholas Beaton MASCOS / University of MelbourneDr Andrea Bedini MASCOS / University of MelbourneMr Andrew Birrell University of QueenslandProf Natashia Boland The University of NewcastleDr Raymond Booth Flinders UniversityProf Jonathan Borwein The University of NewcastleProf Peter Bouwknegt Australian National UniversityProf Richard P Brent Australian National UniversityDr Nathan Brownlowe University of WollongongMr Paul Bryan Australian National UniversityProf Martin Bunder University of WollongongMr Samuel Butler University of SydneyProf Andreas Cap University of ViennaDr Vivien Challis University of QueenslandProf Carl Chiarella University of Technology, SydneyMr Maurice Chiodo The University of MelbourneMs Cath Chisholm University of WollongongDr Florica Cirstea University of SydneyDr Julie Clutterbuck Australian National UniversityMr Matthew Kevin Cooper University of QueenslandProf Michael Cowling University of New South WalesDr Barry Cox University of AdelaideDr Mark Craddock University of Technology, SydneyMr Andrew Crisp University of SydneyProf Edward Norman Dancer University of SydneyDr Daniel Daners University of SydneyDr Pamela Joy Davy University of WollongongDr Jan De Gier The University of MelbourneMr Frank De Silva AMSI/University of MelbourneDr Valentin Deaconu University of Nevada, RenoDr Jim Denier University of AdelaideMr Paul Denny The University of AucklandDr Alice Devillers The University Of Western AustraliaDr Norman Do The University of MelbourneProf Ian Doust University of New South Wales

45

List of Registrants

Dr Jie Du University of New South WalesProf Yihong Du University of New EnglandProf Xuan Duong Macquarie UniversityDr David Easdown University of SydneyDr James East University of Western SydneyProf Michael Eastwood Australian National UniversityProf Andrew Craig Eberhard Royal Melbourne Institute of TechnologyDr Maureen Edwards University of WollongongDr Attila Egri-Nagy University of Western SydneyProf Matthias Ehrgott The Univesrity of AucklandDr Murray Elder The University of NewcastleMr Ali Sayed Elfard University of WollongongProf Demosthenes Ellinas Technical University of CreteDr Faramroze Engineer University of NewcastleMs Mehri Esmaeili Darafshani Monash UniversityMr Nicholas Fewster-Young University of New South WalesDr Mark James Fielding University of WollongongProf Jerzy Filar Flinders UniversityMr Caley Finn The University of MelbourneProf Peter Forrester The University of MelbourneDr Andrew Francis University of Western SydneyProf Vladimir Gaitsgory University of South AustraliaDr Nora Ganter The University of MelbourneDr Timothy Garoni Monash UniversityDr Volker Gebhardt University of Western SydneyDr Alex Ghitza The University of MelbourneMr Matthew Gibson University of SydneyMr Neil Gillespie The University Of Western AustraliaDr Michael Giudici The University Of Western AustraliaDr Joanna Goard University of WollongongDr Ben Goldys University of New South WalesProf Rod Gover AMSIDr Joseph Grotowski The University of QueenslandMr Ivan Guo University of SydneyProf Tony Guttmann The University of MelbourneDr Eldar Hajilarov University of BallaratMrs Joanne Hall Royal Melbourne Institute of TechnologyDr Kais Hamza Monash UniversityMr Alexander Hanysz University of AdelaideMr David Hartley Monash UniversityDr Andrew Hassell Australian National UniversityDr Stuart Hawkins Macquarie UniversityMr Drew Heard AMSI/University of MelbourneDr Anthony Henderson University of SydneyDr Bruce Henry University of New South WalesDr Roslyn Hickson Australian National UniversityMrs Ana Hinic-Galic La Trobe UniversityMr Bao Ho La Trobe UniversityDr Jeffrey Hogan University of NewcastleMr Daniel Horadam University of NewcastleDr Algy Howe Australian National UniversityMr Philip Howes University of SydneyMr Daniel Jackson Monash UniversityDr Simon James Deakin UniversityMrs Sangeeta Jhanjee Monash UniversityDr Qinian Jin Australian National UniversityDr Stuart Johnson University of AdelaideProf Nalini Joshi University of SydneyDr Sooran Kang University of Wollongong

46

List of Registrants

Dr Peter Kim University of SydneyDr Sangjib Kim University of QueenslandMr Justin Koonin University of SydneyMr Matthew Kotros The University of MelbourneDr Alexander Kumjian University of Wollongong/University of Nevada, RenoProf Philip Laird University of WollongongDr Bishnu Lamichhane University of NewcastleMr Mathew Langford Australian National UniversityDr Finnur Larusson University of AdelaideDr Quoc Thong Le Gia University of New South WalesMr Alex Lee The University of MelbourneDr Thomas Leistner University of AdelaideDr Paul Leopardi Australian National UniversityMr Hui Li University of WollongongDr Guanghua Lian Auckland University of TechnologyDr Shuangzhe Liu AMSIDr Barbara Maenhaut The University of QueenslandDr Snigdhayan Mahanta The University of AdelaideDr Peter Malkin BHP BillitonMr Ben Maloney University of WollongongProf Prabhu Manyem Shanghai UniversityDr Robert Marangell University of SydneyProf Timothy Marchant University of WollongongDr Ian Marquette The University of QueenslandProf Hiroshi Matano University of TokyoDr Eduardo Cerutti Mattei The University of QueenslandDr Dillon Mayhew Victoria University of WellingtonMr Anthony Mays The University of MelbourneDr Rupert Gordon McCallum University of New South WalesMr Stephen Michael McCormick Monash UniversityDr James McCoy University of WollongongDr Michaael McCrae AMSIProf Alan McIntosh Australian National UniversityDr Peter McNamara Stanford UniversityDr Christopher Meaney Macquarie UniversityMr Lin-Feng Mei University of New EnglandDr Facundo Memoli University of AdelaideProf Govind Menon Brown UniversityDr Ville Merila University of NewcastleDr Boris Miller Monash UniversityMrs Fatemah Mofarreh University of WollongongMr Amir Moghaddam The University of QueenslandMiss Ajanta Moitra University of Technology, SydneyProf Joel Moitsheki University of the WitwatersrandDr Ross Moore Macquarie UniversityProf Tohru Morimoto Kinki UniversityMr Andrew Morris University of NewcastleDr Eric Mortenson University of QueenslandMr Sudi Mungkasi Australian National UniversityProf Amnon Neeman Australian National UniversityDr Katharina Neusser Australian National UniversityProf Mike Newman Australian National UniversityDr Peter Nickolas University of WollongongProf Rod Nillsen University of WollongongDr Andrew Norton Max Planck Institute for Gravitational PhysicsDr Andriy Olenko La Trobe UniversityDr Todd Oliynyk Monash UniversityMr Wilson Ong Australian National UniversityDr John Ormerod University of Sydney

47

List of Registrants

Mr Omar Ortiz The University of MelbourneDr Judy-anne Osborn University of NewcastleDr James Parkinson University of SydneyDr David Pask University of WollongongDr Laurentiu Paunescu University of SydneyDr Graeme Pettet Queensland University of TechnologyDr Hung Le Pham Victoria University of WellingtonDr Denis Potapov University of New South WalesProf Petrus H Potgieter University of South AfricaProf Cheryl Praeger The University Of Western AustraliaDr Christopher John Price University of CanterburyProf Geoffrey Prince AMSIProf Jacqui Ramagge University of WollongongMr Matthew Randall Australian National UniversityDr Adam Rennie Australian National UniversityMr Tyson Ritter University of AdelaideProf Mick Roberts Massey UniversityProf Tony Roberts University of AdelaideDr Frederic Rochon Australian National UniversityDr Marianito Rodrigo University of WollongongProf John Ryan University of ArkansasMr Parinya Sa Ngiamsunthorn University of SydneyProf John Sader The University of MelbourneDr Katja Sagerschnig Australian National UniversityMr Stephen James Sanchez University of New South WalesDr Caz Sandison University of WollongongDr Sanjiban Santra University of SydneyDr Katherine Anne Seaton La Trobe UniversityProf Jennifer Seberry University of WollongongDr Henry Segerman The University of MelbourneProf Akos Seress The University Of Western AustraliaMr David Stewart Shellard Australian National UniversityDr Alla Shymanska Auckland University of TechnologyDr Aidan Sims University of WollongongDr Brailey Sims University of NewcastleDr Scott Sisson AMSIProf Jan Slovak Masaryk UniversityMr Andrew Graeme Smith University of QueenslandDr Petr Somberg Charles UniversityProf Vladimir Soucek Charles UniversityDr Peter John Stacey La Trobe UniversityDr Elizabeth Stanhope Lewis and Clark College/The University of MelbourneMs Robyn Stuart University of New South WalesDr Steve Sugden Bond UniversityMr Tharatorn Supasiti The University of MelbourneDr Arman Taghavi-Chabert Masaryk UniversityDr Masoud Talebian University of NewcastleDr Don Taylor University of SydneyProf Peter Gerrard Taylor The University of MelbourneMrs Naghmana Tehseen La Trobe UniversityDr Ngamta Thamwattana University of WollongongDr Dennis The Australian National UniversityDr Anne Thomas University of SydneyProf Kenneth Paul Tod University of OxfordMs Maureen Townley-Jones University of NewcastleMs Thi Dinh Tran University of New South WalesMr Thien Tran-Duc University of WollongongDr Dimetre Triadis La Trobe UniversityMs Maria Tsarenko The University of Melbourne

48

List of Registrants

Mr James Wan University of NewcastleDr Bryan Wang Australian National UniversityProf Xu-Jia Wang Australian National UniversityProf You-Gan Wang University of QueenslandDr Samuel Webster University of WollongongDr Martin Wechselberger University of SydneyDr Craig Westerland The University of MelbourneDr Michael Whittaker University of WollongongProf George Willis The University of NewcastleMr Shane Wilson ING AustraliaDr Leigh Wood Macquarie UniversityProf Ruibin Zhang University of SydneyDr Tonghua Zhang Swinburne University of TechnologyProf Song-Ping Zhu University of WollongongDr Wadim Zudilin The University of Newcastle

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Abstracts

0. Plenaries 52

1. Algebra and Number Theory 54

2. Calculus of Variations and Partial Differential Equations 58

3. Computational Mathematics 61

4. Aspects of Applications in Mathematics 63

5. Operator Algebras and Noncommutative Geometry 68

6. Optimisation 70

7. Geometry and Topology 73

8. Topological Groups and Harmonic Analysis 77

9. Financial Mathematics 79

10. Combinatorics 81

11. Probability and Statistics 83

12. General session 85

13. Mathematical Physics 87

14. Differential Geometry 90

15. Education Afternoon 93

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0. Plenary

0.1. Geometric Asymptotics or “How I learnt tostop worrying and love exceptional Lie groups”

Nalini Joshi (University of Sydney)

11:30 Mon 26 September 2011 – Hope Theatre

Nalini Joshi

At the heart of models of contemporary scienceare highly transcendental solutions of integrablesystems whose mathematical description remainsincomplete. They form the core of modern specialfunction theory, which will shape the success andfailure of scientific models for decades to come.In this talk, I will explain what we know aboutthese functions and describe a new mathematicaltheory that is expected to dramatically improveour understanding of these functions.

0.2. Penrose’s Weyl Curvature Hypothesis and hisConformal Cyclic Cosmology

Kenneth Paul Tod (University of Oxford)

14:00 Mon 26 September 2011 – Hope Theatre

Kenneth Paul Tod

Penrose’s Weyl Curvature Hypothesis, which datesfrom the late 70s, is a hypothesis, motivated byobservation, about the nature of the Big Bangas a singularity of the space-time manifold. HisConformal Cyclic Cosmology is a remarkable sug-gestion, made a few years ago and still being ex-plored, about the nature of the universe, in thelight of the current consensus among cosmologiststhat there is a positive cosmological constant. Ishall review both sets of ideas within the frame-work of general relativity, and emphasise how thesecond set solves a problem posed by the first.

0.3. How mathematics can help to measure atomicscale phenomena, design spacecraft and predict theflow of ornate water fountains

John Sader (The University of Melbourne)

09:00 Tuesday 27 September 2011 – Hope Theatre

John E. Sader

The art of applied mathematics lies in identify-ing the essential features of a “real-life” problem.This then leads to its abstraction to a mathemat-ical formulation from which the underlying mech-anisms and their consequences can be analysed.In this talk, I will give an overview of some ofthe applied mathematics my group is conduct-ing in fields related to nanotechnology, classicalfluid dynamics and space technology. I will en-deavour to show that simple mathematical ideascan contribute to advances in modern technologyand understanding of seemingly complex physicalphenomena. Specifically, I will give an overviewof work dealing with advancing the technological

infrastructure of atomic scale measurements, un-derstanding the design of hypersonic vehicles usedfor atmospheric entry of planetary probes, and ex-plaining why ornate flows are generated by direct-ing a jet (such as that emitted from a garden hose)onto a flat ceiling.

0.4. Algebraic K-theory via the trace method

Vigleik Angeltveit (Australian National University)


Vigleik Angeltveit

Algebraic K-theory is important in many differentfields: algebraic geometry, number theory, geo-metric topology, and of course algebraic topology.

The algebraic K-theory of a ring lives in stable ho-motopy theory and is extremely difficult to com-pute directly from the definition. But there is acomparison map to topological Hochschild homol-ogy, which is often easier to understand.

In my talk I will attempt to outline how one canuse this comparison map to understand algebraicK-theory, and give some recent examples of in-stances where this approach has been successful.Parts of what I will be talking about is joint workwith Teena Gerhardt and/or Lars Hesselholt.

0.5. PUBLIC LECTURE: The mathematics ofepidemics and pandemics



Mick Roberts

This talk will describe how mathematical mod-els may be used to explain the dynamics of infec-tious diseases, especially those caused by a virus.The measles vaccination schedule in New Zealandwas redesigned in 2001 using a model, and therehave been no further epidemics. Mosquito-borneviruses such as dengue are spreading into new re-gions due to climate change. Other viruses, likeinfluenza and HIV, are difficult to bring undercontrol, as they evolve rapidly to avoid the im-mune response. Mathematical models help us tounderstand epidemiology and guide public healthinterventions. I will explain how these modelsare constructed and analysed, using a minimumof mathematics.

0.6. Totally disconnected, locally compact groups

George Willis (The University of Newcastle)

09:00 Wednesday 28 September 2011 – Hope Theatre

George Willis

Locally compact groups appear in many branchesof mathematics and their rich theory lends themtheir own intrinsic interest. It was shown by A.

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1. Plenary

Haar and A. Weil that locally compact groupsare precisely those that support a translation-invariant measure, which has the further impactthat they are also the class of groups to whichmethods of harmonic analysis naturally extend.

Study of the structure of locally compact groupsfalls into two cases: connected groups, which ap-pear as symmetries of smooth structures suchas spheres for example; and totally disconnectedgroups, which appear as symmetries of discretestructures such as trees, as well as in number the-oretic and algebraic contexts.

While the understanding of connected groupswas essentially completed with the solution ofHilbert’s Fifth Problem in the 1950’s, the theoryof totally disconnected groups is now at an excit-ing stage where enough has been discovered thatthe outlines of a full structure theory may dimlybe seen but where many blank spaces remain.

The lecture will survey recent advances in the un-derstanding of totally disconnected, locally com-pact groups. These include: general tools thatpartially fill the role played by linear methodsin the theory of Lie groups; applications of thesemethods in algebra and geometric group theory;and work on the classification of simple totally dis-connected groups. Future directions for researchand areas where discoveries remain to be madewill be indicated.

0.7. Traveling waves in a sawtoothed cylinder andtheir homogenization limit

Hiroshi Matano (University of Tokyo)

14:00 Wednesday 28 September 2011 – Hope Theatre

Hiroshi Matano

My talk is concerned with a curvature-dependentmotion of plane curves in a two-dimensional cylin-der with spatially undulating boundary. The lawof motion is given by

V = κ+A,

where V is the normal velocity of the curve, κ isthe curvature, and A is a positive constant. Theboundary undulation is assumed to be recurrent.In other words, the boundary has many bumpsthat are aligned in a spatially recurrent manner.This includes periodic and quasi-periodic undula-tions as special cases.

We discuss how the average speed of the travel-ing wave depends on the geometry of the domainboundary. We will first give a necessary and suf-ficient condition for a traveling wave to exist. Wethen show that traveling waves have well-definedaverage speed if the undulation is uniquely er-godic.

Next we present an example of traveling wavewhose average speed is zero. Such a peculiar situ-ation, which we call “virtual pinning”, can occuronly in non-periodic environments.

We then consider the homogenization problem asthe boundary undulation becomes finer and finer,and determine the homogenization limit of the av-erage speed and the limit profile of the travelingwaves. Quite surprisingly, this homogenized speeddepends only on the maximal opening angles ofthe domain boundary and no other geometricalfeatures are relevant.

We also estimate the rate of convergence of thetraveling wave speed to its homogenization limit.It turns out that this convergence rate is pre-cisely O(

√ε) when the boundary undulation is

periodic, while it is slower in the aperiodic case,where ε is a parameter that represents the typicalscale of the boundary undulation. In a more gen-eral case where the boundary undulation is quasi-periodic with m independent frequencies, our pre-liminary analysis suggests that the convergencerate is O(ε2/(m+3)), with some logarithmic cor-rections. This formula shows that the convergencebecomes slower as m increases.

This is joint work with Bendong Lou and Ken-IchiNakamura.

0.8. Mathematical models for the evolution andtransmission of a virus


09:00 Thursday 29 September 2011 – Hope Theatre

Mick Roberts

The influenza virus evolves through gradual mu-tation, causing antigenic drift. This enables thevirus to compromise the effectiveness of the im-mune system. Less frequently, a reassortmentleads to an antigenic shift, followed by a pandemicsuch as that of H1N1 (swine flu) in 2009. TheHIV virus evolves within the host, forming ‘es-cape mutants’ that are not recognised by the im-mune system. Mathematical models may be usedto describe and explain these processes, and to de-vise strategies for the control or elimination of theinfection. In addition, models are now routinelyused for predicting the public health requirementsof epidemics of emerging infections.

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1.1. Endomorphism algebras of modular motives

Debargha Banerjee (Australian National

University)

12:30 Thursday 29 September 2011 – 24.104

Debargha Banerjee / Eknath Ghate

We will show the endomorphism algebras of Mod-ular motives are related to a suitable lifts of themodular forms.

1.2. Lucas Functions and Sums of Powers ofIrrationals

Martin Bunder (University of Wollongong)

10:30 Tuesday 27 September 2011 – 24.104

Martin Bunder

Lucas functions Un(P,Q) satisfy:

U0(P,Q) = 0, U1(P,Q) = 1,

Un+1(p,Q) = PUn −QUn−1(P,Q).

We show that for any positive integer m, there areintegers h, k, th, . . . , tk such that for all positiveintegers n and a range of values of integers P andQ:

mUn(P,Q) = Σki=htiUn+i(P,Q),

where Σsi=htiUn+i(P,Q) < Un+s+1(P,Q) for h ≤s ≤ k. Also m = Σki=htic

i, for c = 1/2(P =

±√P 2 − 4Q). Several results in this paper can

be generalised to Horadam functions.

1.3. An exotic Springer correspondence

Andrew Crisp (University of Sydney)


Andrew Crisp

The Springer Correspondence is a deep result inalgebraic geometry which establishes a connectionbetween orbits of nilpotent elements in a Lie alge-bra and the irreducible representations of its as-sociated Weyl group. An “exotic” bijective corre-spondence for type C is achieved by consideringthe action of the symplectic group on a differentvariety, the exotic nilpotent cone. I will presentmy work in describing an analogue for type F,highlighting the octonionic origins of the excep-tional Lie algebras and the interesting challengesinvolved in constructing and exploring this repre-sentation.

1.4. Representations of Affine q-Schur Algebras

Jie Du (University of New South Wales)


Jie Du

We establish an isomorphism from the quantum

loop algebra UC(gln) with Drinfeld’s new presen-tation to the double Ringel–Hall algebra associ-ated with a cyclic quiver 4(n) and an explicithomomorphism from the double Ringel–Hall al-gebra to an affine q-Schur algebra S4(n, r)C. Weuse them to link polynomial representations of

UC(gln) with representations of S4(n, r)C. Thus,using Chari-Pressley’s classification of finite di-

mensional representations of UC(sln) and its gen-eralization to irreducible polynomial representa-

tions of UC(gln) by Frenkel and Mukhin, weare able to classify irreducible representationsof S4(n, r)C in terms of Drinfeld’s polynomials,when the parameter q is not a root of 1. Onthe other hand, using the classification of irre-ducible representations of the affine Hecke alge-bra H4(r)C associated with an affine symmetricgroup by Zelevinsky and Rogawski, we obtain an-other classification of irreducible representationsof S4(n, r)C in terms of multi-segments. Whenn > r, we identify the two classifications by an ex-plicit map from multi-segments to Drinfeld’s poly-nomials.

This is joint work with Bangming Deng and QiangFu.

1.5. Defining relations for idempotent generatorsin finite semigroups of mappings

James East (University of Western Sydney)


James East

John Howie showed in 1966 that any non-bijectivefunction from a finite set to itself can be obtainedby composing a number of idempotent functions.In semigroup theoretic terms, this says that thesingular part of a finite transformation semigroupis generated by its idempotents. I’ll present a setof defining relations for this singular subsemigroupwith respect to the generating set consisting of allcorank 1 idempotents. Along the way, I’ll also dis-cuss some other extensions of Howie’s results inthe context of partial transformation semigroups,Brauer monoids, partition monoids, semigroups ofinteger matrices, and semigroups of transforma-tions of various kinds of spaces. If time permits,I’ll say something about the infinite case.

1.6. Dependency Functions in Hierarchical(De)Compositions of Finite TransformationSemigroups

Attila Egri-Nagy (University of Western Sydney)


Attila Egri-Nagy

54


Turning around the decompositions of finite trans-formation semigroups (Krohn-Rhodes Theory) westart from a fixed list of transformation semi-groups

(X1, S1), . . . , (Xn, Sn)

and build cascaded structures (substructures ofthe wreath product). Operations in the hierarchi-cal structure are described as a tuple of functions(d1, . . . , dn) where a dependency function di (oflevel i) is a function

di : X1 × . . .×Xi−1 → Si i ∈ 1 . . . n.Algebraically these encode an action on trees andfrom an algorithmic viewpoint these functions andtheir combinatorial properties are the prime ob-jects of study. Here we summarize the basic prop-erties of dependency functions in hierarchical de-compositions (real dependence, monomial gener-ators, etc.) and outline the most important ques-tions that are needed for dealing with decomposi-tions. In general, we ask how and to what extentthe local properties of the dependency functionsdetermine the global properties of the compositestructure.

1.7. New results about Baumslag-Solitar groups

Murray Elder (The University of Newcastle)

12:30 Wednesday 28 September 2011 – 24.104

Murray Elder

I will discuss some new results about this class ofgroups.

1.8. Characters of categorical representations

Nora Ganter (The University of Melbourne)


Nora Ganter, Mikhail Kapranov

Let G be a finite group. The notion of represen-tation of G by functors on a category V goes backto Grothendieck. More generally, one can con-sider representations of G by 1-automorphisms ofan object V in a 2-category.

We introduce and study the character theory ofsuch representations. The talk will give a short in-troduction to the subject and then dive into someapplications.

1.9. Lifting modular forms

Alex Ghitza (The University of Melbourne)


Alex Ghitza and Scott Mullane

We discuss applications of vanishing theorems forsheaf cohomology to the question of relating thespaces of modular forms (mod p) and spaces ofmodular forms in characteristic zero.

1.10. Generalised quadrangles with a group actingprimitively on points and lines

Michael Giudici (The University Of Western

Australia)


Michael Giudici

Generalised polygons were introduced by Tits as amodel for studying the simple groups of Lie typeof rank 2. A generalised quadrangle is an inci-dence structure of points and lines such that thebipartite incidence graph has diameter 4 and girth8. The classical examples are the low dimensionalpolar spaces associated with the classical groupsPSp(4, q), PSU(4, q) and PSU(5, q), and their du-als. In this talk I will discuss recent work aimedat characterising the classical examples in terms ofthe action of their automorphism group on pointsand lines. This is joint work with John Bamberg,Joy Morris, Gordon Royle and Pablo Spiga.

1.11. Structure of Hjelmslev planes over Galoisrings.

Joanne Hall (Royal Melbourne Institute of

Technology)

17:00 Mon 26 September 2011 – 24.104

Joanne Hall, Asha Rao, Diane Donovan

Hjelmslev planes are a geometric structure withemerging applications in coding theory and quan-tum cryptography. Projective Hjelmslev planesare a generalisation of projective planes. Just assome projective planes can be constructed usinga field, some Hjelmslev planes can be constructedusing rings. We investigate the structure of a pro-jective Hjelmslev plane over a Galois ring.

1.12. Small representations and the affineGrassmannian

Anthony Henderson (University of Sydney)


Pramod Achar and Anthony Henderson

Let G be a simple algebraic group over the com-plex numbers. For any irreducible representationV of G, the zero weight space V T of V carries arepresentation of the finite Weyl group W . Thisis known to be particularly nice when V is small,meaning that no weight of V is twice a root ofG. For example, when G = PGLn and V issmall, V T is an irreducible representation of Sn,and all irreducible representations of Sn arise inthis way. I will explain the geometric significanceof smallness, and how the small part of the affineGrassmannian of the dual group G∨ (geometrizingrepresentations of G) can be explicitly related toits nilpotent cone (geometrizing representations ofW ).

55


1.13. Fractal Groups and Automata

Daniel Horadam (University of Newcastle)


Daniel Horadam

Fractal groups are a class of self-similar groupswhich act by automorphisms on a regular rootedtree. They play an important role in the struc-ture theory of totally disconnected locally com-pact groups. In this talk I will present some exam-ples and interesting properties of fractal groups, inparticular those which are generated by finite au-tomata, and discuss how they might be classified.

1.14. Various generalisations of minimax theoremusing Clifford algebras

Sangeeta Jhanjee (Monash University)


Sangeeta Jhanjee

The minimax principle or Courant-Fischer-Weylminimax principle provides a variational charac-teristisation of all eigenvalues. It is one of themost powerful tools in the investigation of thespectrum. In this talk, I would like to presentvarious generalisations of minimax theorem usingClifford algebras.

1.15. Toplogy of eigenspace posets for unitaryreflection groups

Justin Koonin (University of Sydney)

16:30 Mon 26 September 2011 – 24.104

Justin Koonin

The eigenspace theory of unitary reflection groups,initiated by Springer and Lehrer, suggests thatthere are analogues for reflection groups (in factfor all linear groups) of the Quillen complex of p-subgroups of a finite group. We investigate topo-logical properties of these complexes, and the rep-resentations of reflection groups on their homol-ogy.

This talk will serve as an introduction to posettopology and its application to representation the-ory, and will also present new results which extendthe well-known work of Orlik and Solomon on hy-perplane arrangements.

1.16. Diophantine approximation of q-continuedfractions

Ville Merila (University of Newcastle)


Ville Merila

In his notes Ramanujan studied, among manyother topics, certain continued fractions whosepartial numerators and denominators are polyno-mials in parameter q, (usually |q| < 1). Many ofthese q-continued fractions have a rich structure

for their connections to (number theoretic) func-tions such as (partial) theta function and partitionfunction. In this talk we shall consider a wideclass of q-continued fractions from the viewpointof Diophantine approximation. Some special casescomprise for example Ramanujan, Ramanujan-Selberg, Eisenstein and Tasoev’s continued frac-tions with sharp irrationality measures.

1.17. An Alternative Proof of Hesselholt’sConjecture on Galois Cohomology of Witt Vectorsof Algebraic Integers

Wilson Ong (Australian National University)


Wilson Ong

Let K be a complete discrete valuation field ofcharacteristic zero with residue field kK of char-acteristic p > 0. Let L/K be a finite Galois ex-tension with Galois group G = Gal(L/K) andsuppose that the induced extension of residuefields kL/kK is separable. Let Wn(·) denote thering of p-typical Witt vectors of length n. Hes-selholt conjectured that the pro-abelian groupH1(G,Wn(OL))n≥1 is isomorphic to zero. Hogadiand Pisolkar have recently provided a somewhatlengthy proof of the conjecture. In this paper,we provide a considerably shorter proof of Hessel-holt’s conjecture.

1.18. Homogeneous Spaces of p-Compact Groups

Omar Ortiz (The University of Melbourne)


Omar Ortiz, Arun Ram, Craig Westerland

p-compact groups are the topological realizationof complex reflection groups. In this talk we willfocus in the object analogous to the flag varietyin this setting and describe its cohomology usingtechniques from moment graph theory.

1.19. A complete classification of commutativeparabolic Hecke algebras

James Parkinson (University of Sydney)


James Parkinson

In this talk we describe a complete classification ofcommutative parabolic Hecke algebras (for Cox-eter groups of arbitrary type, and arbitrary par-abolic subgroups). In finite type, for example,these algebras arise as centraliser rings of inducedpermutation representations of finite groups of Lietype, and as such have a long and rich history.This is joint work with Peter Abramenko (Vir-ginia) and Hendrik Van Maldeghem (Ghent).

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1.20. Legendre Polynomials and Ramanujan-likeseries for 1/π

James Wan (University of Newcastle)

16:00 Mon 26 September 2011 – 24.104

James Wan, Heng Huat Chan, Wadim Zudilin

In 1914, Ramanujan produced rational series for1/π times a quadratic irrational; ever since suchseries have been a source of fascination. Inspiredby the recent conjectures of Z. W. Sun and G.Almkvist, we present a recipe for producing verygeneral series for 1/π in the spirit of Ramanujan.

In our resolution of the conjectures, we derive anew generating function for the rarefied Legendrepolynomials, using some well-known results (suchas Bailey’s identity) as well as a ‘forgotten’ re-sult due to F. Brafman. Followed by significantamount of computer experimentation, and draw-ing from the theory of modular forms and hyper-geometric series, we are able to prove rather un-expected links between the Legendre polynomials,Apery-like sequences, and 1/π.

This talk is based on joint work with Heng HuatChan and Wadim Zudilin.

1.21. Ramanujan-style mathematics for Mahlermeasures

Wadim Zudilin (The University of Newcastle)

15:00 Mon 26 September 2011 – 24.104

Wadim Zudilin

In my talk I will review some recent progress onevaluations of Mahler measures via hypergeomet-ric series and Dirichlet L-series. I will providemore details for the case of the Mahler measure of1 + x + 1/x + y + 1/y, whose evaluation was ob-served by C. Deninger and conjectured by D. Boyd(1997). The main ingredients are relations be-tween modular forms and hypergeometric seriesin the spirit of Ramanujan. The talk is based onjoint work with Mat Rogers.

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2.1. The Kato square root problem on vectorbundles of generalised bounded geometry

Menaka Lashitha Bandara (Australian National

University)

16:30 Mon 26 September 2011 – 24.103

Lashi Bandara and Alan McIntosh

We consider complete Riemannian manifolds whichare exponentially locally doubling and formulate anotion of generalised bounded geometry for vectorbundles over such manifolds. We prove quadraticestimates for perturbations of Dirac type opera-tors on such bundles, and hence obtain a Katosquare root type estimate under an appropriateset of assumptions. Furthermore, we show thatunder uniform Ricci curvature bounds and uni-form lower bounds on injectivity radius, a Katosquare root estimate can be obtained for certaincoercive operators over the bundle of finite ranktensors. Lastly, we show that this coercivity con-dition is automatically satisfied for scalar-valuedfunctions.

2.2. Isoperimetric comparison techniques for Ricciflow on surfaces and curve shortening flow

Paul Bryan (Australian National University)

16:00 Mon 26 September 2011 – 24.103

Paul Bryan, Ben Andrews

I will describe a comparison technique for theisoperimetric profile of surfaces evolving by nor-malised Ricci flow and for the interior of closedcurves evolving by normalised curve shorteningflow. From this technique, we obtain explicit cur-vature bounds leading directly to convergence toa minimising (e.g. constant curvature) configura-tion.

2.3. On the classification of isolated singularitiesfor nonlinear elliptic equations

Florica Cirstea (University of Sydney)


Florica C. Cirstea

In this talk we discuss a broad class of nonlin-ear elliptic equations in a punctured domain andgive a complete classification of the behaviournear an isolated singularity for all positive so-lutions. An important feature of our study liesin the incorporation of inverse square potentialsand weighted nonlinearities, whose asymptotic be-haviour is modeled by regularly varying func-tions. In particular, we find sharp conditionssuch that the singularity is removable for all non-negative solutions, thus resolving an open ques-tion of Vazquez and Veron (1985).

2.4. Optimal bounds for the first Neumanneigenvalue on a manifold

Julie Clutterbuck (Australian National University)

15:30 Mon 26 September 2011 – 24.103

Julie Clutterbuck (joint work with Ben Andrews)

We use gradient bounds to find a new proof ofthe optimal lower bound for the first Neumanneigenvalue on a manifold with bounds on the Riccicurvature.

2.5. Large interaction problems for non-linearP.D.E.

Edward Norman Dancer (University of Sydney)


Edward Norman Dancer

We discuss large interaction problems for certainsystems of nonlinear elliptic and parabolic equa-tions.These occur in both populations models inbiology and nonlinear optics. We show that thereis a limit problem when the interaction is largeand the different nonlinearities in the two prob-lems give the same limit problem. We also dis-cuss the regularity of the limit problem and esti-mates for solutions which are uniform in the largeparameter. This is joint work with my postdocKelei wang and Zhitao Zhang (Chinese Academyof Sciences)

2.6. An isoperimetric inequality related to aBernoulli problem

Daniel Daners (University of Sydney)


Daniel Daners

Given a bounded domain Ω ⊂ RN we look atthe minimal parameter Λ(Ω) for which a Bernoullifree boundary value problem for the p-Laplacianhas a solution minimising an energy functional.We show that amongst all domains of equal vol-ume Λ(Ω) is minimal for the ball. Moreover, weshow that the inequality is sharp with essentiallyonly the ball minimising Λ(Ω). This is joint workwith Bernd Kawohl.

2.7. Propagation in a time-periodic nonlineardiffusion problem with free boundary

Yihong Du (University of New England)


Yihong Du

We consider the diffusive logistic equation withfree boundary in time-periodic environment. Sucha problem describes the spreading of a new or

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invasive species. We demonstrate a spreading-vanishing dichotomy and determine the asymp-totic spreading speed when spreading occurs.This is joint work with Zongming Guo and RuiPeng.

2.8. Existence of solutions to second ordernonlinear singular boundary value problems.

Nicholas Fewster-Young (University of New South

Wales)


Nicholas Fewster-Young

This talk examines the existence of solutions tononlinear singular boundary value problems. Thisarea of differential equations has many applica-tions in physical sciences, for example thermal ex-plosions, electrohydrodynamics and radially sym-metric nonlinear diffusion in the n-dimensionalsphere. The results presented build on the workof P. Hartman and D. O’Regan, and improve onthe current results. The method of proving theseresults relies on obtaining a priori bounds on allsolutions to the problem and using O’Regan exis-tence theorems to prove existence of solutions.

2.9. New Boundary Regularity Results for EllipticSystems.

Joseph Grotowski (The University of Queensland)


Joseph Grotowski

We consider quasilinear elliptic systems of diver-gence type, with inhomogeneity obeying the nat-ural growth condition. We consider some recentresults on parrtial regularity at the boundary un-der various boundary conditions.

2.10. Study of Mean Curvature Flow Equationsusing Functional Analysis

David Hartley (Monash University)


David Hartley

Geometric evolution equations play an importantrole in the study of manifolds. One of the mostfamous evolution equations is where the surfacemoves at a speed proportional to the mean cur-vature. The resulting PDE is a heat equationand as such smooths the surface. For mean cur-vature flow equations one of the most importantresults is determining when a surface will convergeto sphere. In this talk I discuss star-shaped sur-faces moving via mean curvature flow equationsby considering them as ODEs in an abstract Ba-nach space.

2.11. Dain’s variational principle and its relation toan angular momentum-mass inequality in generalrelativity

Stephen Michael McCormick (Monash University)

17:00 Mon 26 September 2011 – 24.103

Stephen Michael McCormick

In 2008, Dain used a variational argument toprove that the extreme Kerr solution is a uniqueabsolute minimum of the mass functional amonga large class of vacuum, maximal, asymptoticallyflat, axisymmetric initial data for the Einsteinequations with fixed angular momentum. In thistalk I intend to provide an overview of Dain’sconstruction and how this variational argumentwas first used to prove that among all ’momen-tarily stationary’, asymptotically flat, axisymmet-ric vacuum solutions; critical points of the masscoincide with stationary solutions. Furthermore,if an absolute minimum exists amongst maximal,asymptotically flat, axisymmetric vacuum solu-tions; then that solution is also ’momentarily sta-tionary’.

2.12. Fully nonlinear curvature flow withnonconvex initial data

James McCoy (University of Wollongong)


James McCoy

I will consider initial hypersurfaces which are notnecessarily convex moving under second orderfully nonlinear curvature flow. I’ll describe recentjoint work with Ben Andrews and Mat Langfordon non-collapsing of evolving hypersurfaces andsome related results.

2.13. Finite Speed of Propagation for First OrderSystems and Second Order Operators

Alan McIntosh (Australian National University)

15:00 Mon 26 September 2011 – 24.103

Alan McIntosh

For a self adjoint first order system D withbounded principal symbol, acting on a completeRiemannian manifold M , it is known that thegroup eitD has finite speed of propagation. Bythis it is meant that if u has support in a compactset K, then eitDu has support in KC|t| = y ∈M ; dist(y,K) ≤ C|t| for some constant C. Ishall present a new proof of this result, at the sametime showing that the result holds more generally,with the self-adjointness assumption weakened tothe requirement that D generates a C0 group sat-isfying ‖eitD‖ ≤ ceκ|t| for some constants c andκ.

I also present implications of this result concern-ing Huygen’s principle for second order wave equa-tions. This is recent joint research with AndrewMorris.

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2.14. On a nonlocal equation modellingphytoplankton growth

Lin-Feng Mei (University of New England)


Linfeng Mei

We consider a nonlocal differential equation aris-ing from phytoplankton dynamics. The existence,uniqueness, dynamic behaviour, as well as the lim-iting profiles as certain parameters are in extremecases are investigated. This is based on a jointpaper with Yihong Du.

2.15. There are no magnetically chargedparticle-like solutions of the Einstein-Yang-Millsequations for models with Abelian residual groups

Todd Oliynyk (Monash University)


Todd Oliynyk

According to a conjecture from the 90s, glob-ally regular, static, spherically symmetric (i.e.particle-like) solutions with nonzero total mag-netic charge are not expected to exist in Einstein-Yang-Mills theory. In this talk, I will describerecent work done in collaboration with M. Fisherwhere we establish the validity of this conjectureunder certain restrictions on the residual gaugegroup. Of particular interest is that our non-existence results apply to the most widely studiedmodels with Abelian residual groups.

2.16. Asymptotics of complete Kahler metrics offinite volume on quasiprojective manifolds

Frederic Rochon (Australian National University)


Frederic Rochon and Zhou Zhang

Let X be a quasiprojective manifold given by thecomplement of a divisor D with normal cross-ings in a smooth projective manifold X. Usinga natural compactification of X by a manifold

with corners X, we describe the full asymptoticbehavior at infinity of certain complete Kahlermetrics of finite volume on X. When these met-rics evolve according to the Ricci flow, we provethat such asymptotic behaviors persist at latertime by showing the associated potential func-tion is smooth up to the boundary on the com-

pactification X. However, when the divisor D issmooth with KX+[D] > 0 and the Ricci flow con-verges to a Kahler-Einstein metric, we show thatthis Kahler-Einstein metric has a rather differentasymptotic behavior at infinity, since its associ-ated potential function is polyhomogeneous within general some logarithmic terms occurring in itsexpansion at the boundary.

2.17. Persistence of bounded solutions of parabolicequations under domain perturbation

Parinya Sa Ngiamsunthorn (University of Sydney)


Parinya Sa Ngiamsunthorn

We study the behaviour of bounded solutions (so-lutions that are defined for all time t ∈ (−∞,∞)and are bounded in a suitable function space)of parabolic equations under perturbation of theunderlying domain. We prove some convergenceresults for bounded solutions of linear parabolicequations in the L2 and the Lp-settings. In ad-dition, we study the persistence of a class ofbounded solutions which decay to zero at t→ ±∞of semilinear parabolic equations under domainperturbation.

2.18. Asymptotic behavior of the least energysolution of a problem with competing powers

Sanjiban Santra (University of Sydney)


Sanjiban Santra

We consider the problem ε2∆u−uq+up = 0 in Ω,u > 0 in Ω, u = 0 on ∂Ω. Here Ω is a smoothbounded domain in RN , 1 < q < p < N+2

N−2 ifN ≥ 3 and ε is a small positive parameter. Westudy the asymptotic behavior of the least energysolution as ε goes to zero in the case q ≤ N

N−2 . Weshow that the limiting behavior is dominated bythe singular solution ∆G−Gq = 0 in Ω\P, G =0 on ∂Ω. The reduced energy is of nonlocal type.

2.19. Regularity of elliptic and parabolic equationalong a vector field

Xu-Jia Wang (Australian National University)


Xu-Jia Wang

By a perturbation argument we study the regu-larity of solutions in a given direction, assumingthat the coefficients and inhomogeneous term areHolder continuous in the direction.

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3.1. Mahler measures, short walks and log-sineintegrals: A case study in hybrid computation

Jonathan Borwein (The University of Newcastle)

11:30 Tuesday 27 September 2011 – 24.G01

Jonathan Borwein and Armin Straub

Abstract: The Mahler measure of a polynomial ofseveral variables has been a subject of much studyover the past thirty years. Very few closed formsare proven but many more are conjectured. Weprovide systematic evaluations of various higherand multiple Mahler measures using moments ofrandom walks and values of log-sine integrals. Wealso explore related generating functions for thelog-sine integrals and their generalizations.

This work, which is joint with Armin Straub,would be impossible without extensive symbolicand numeric computations. It also makes frequentuse of the new NIST Handbook of MathematicalFunctions.

My intention is to show off the interplay betweennumeric and symbolic computing while exploringthe three topics in title.

3.2. Implementing a topology optimisationalgorithm on the GPU

Vivien Challis (University of Queensland)


Vivien Challis

The release of NVIDIA’s CUDA architecture andlanguage CUDA C puts the use of massively par-allel Graphical Processing Units (GPUs) withinthe reach of the scientific programmer, placinglarge computational power at their finger tipsfor little cost. I’ll discuss my experiences re-writing our Fortran 90 topology optimisation al-gorithm using CUDA C. Our algorithm utilisesboth finite difference and finite element meth-ods, which are well-suited to the GPU architec-ture. I’ll demonstrate the speed-ups attainableon consumer-grade GPUs compared to our tra-ditional CPU implementation and highlight thelessons I’ve learned about scientific computing us-ing GPUs.

3.3. A fully discrete Galerkin algorithm for highfrequency exterior acoustic scattering in threedimensions

Stuart Hawkins (Macquarie University)


Stuart C. Hawkins and M. Ganesh

Surface integral equation reformulations of wavepropagation models are the industrial standard

to simulate scattering by three dimensional bod-ies. However, for high frequency scattering, stan-dard discretization techniques for surface integralequations are inefficient for three dimensional ex-terior scattering simulations because they requirea fixed number of unknowns per wavelength ineach dimension, leading to very large CPU timeand memory requirements.

In this talk we describe an efficient surface integralequation algorithm for simulating high frequencyacoustic scattering by three dimensional convexobstacles. Using a powerful integratation schemefor highly oscillatory integrals and globally sup-ported high order basis functions, we demonstratethe high order accuracy and efficiency of our al-gorithm for scatterers with tens of thousands ofwavelengths in diameter. Our algorithm requiresonly mild growth in the number of unknowns andCPU time as the wavenumber increases.

3.4. Inexact Newton regularization methods

Qinian Jin (Australian National University)

15:30 Mon 26 September 2011 – 24.G01

Qinian Jin

Inverse problems arise whenever one searches forunknown causes based on observation of their ef-fects. Such problems are usually ill-posed in thesense that their solutions do not depend continu-ously on the data. In practical applications, onenever has the exact data; instead only noisy dataare available due to errors in the measurements.Thus, the development of stable methods for solv-ing inverse problems is an important topic.

The inexact Newton regularization methods havebeen initiated by Hanke and then generalizedby Rieder to solve nonlinear inverse problems inHilbert spaces. Each of these methods consists oftwo components: an outer Newton iteration andan inner scheme providing increments by regular-izing local linearized equations. An approximatesolution is output by a discrepancy principle. Al-though numerical simulation indicates that theyare quite efficient, it is a longstanding questionthat if these methods are order optimal. I will re-port our recent work and confirm that the meth-ods indeed are order optimal.

In some situations, methods formulated in Hilbertspace setting may not produce good results sincethey tend to smooth the solutions and thus de-stroy the special feature in the exact solution. Bymaking use of the duality mappings and the Breg-man distance we will formulate the inexact New-ton regularization methods in Banach spaces andgive the convergence analysis.

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3.5. A Stabilized Mixed Finite Element Method forthe Biharmonic Equation Based on BiorthogonalSystems

Bishnu Lamichhane (University of Newcastle)

15:00 Mon 26 September 2011 – 24.G01

Bishnu Lamichhane

We propose a stabilized finite element methodfor the approximation of the biharmonic equationwith clamped boundary condition. The mixed for-mulation of the biharmonic equation is obtainedby introducing the gradient of the solution anda Lagrange multiplier as new unknowns. Work-ing with a pair of bases forming a biorthogonalsystem, we can easily eliminate the gradient ofthe solution and the Lagrange multiplier from thesaddle point system leading to a positive definiteformulation. Using a super-convergence propertyof a gradient recovery operator, we prove an op-timal a priori estimate for the finite element dis-cretization for a class of meshes.

3.6. Solving parabolic equations on the unit spherevia Laplace transforms

Quoc Thong Le Gia (University of New South

Wales)

16:00 Mon 26 September 2011 – 24.G01

Quoc Thong Le Gia and William McLean

We propose a method to construct numerical so-lutions of parabolic equations on the unit sphere.The time discretisation uses Laplace transformsand quadrature. The spatial approximation ofthe solution employs radial basis functions (RBFs)restricted to the sphere. The method allows usto construct high accuracy numerical solutions inparallel. In this work, we establish the L2 errorestimates for the cases of smooth and nonsmoothinitial data. Some numerical experiments are alsopresented

3.7. Can compatible discretization, finite elementmethods, and discrete Clifford analysis be fruitfullycombined?

Paul Leopardi (Australian National University)


Paul Leopardi

This talk describes work in progress, towards theformulation, implementation and testing of com-patible discretization of of differential equations,using a combination of Finite Element ExteriorCalculus and discrete Geometric Calculus / Clif-ford analysis. Much work has been done in thetwo seemingly separate areas of the Finite Ele-ment Method and Geometric Calculus for over 42years, and the first part of this talk briefly de-scribes some of this work. The combination of thetwo methods could be called Finite Element Geo-metric Calculus (FEGC). The second part of the

talk gives a tentative description of what FEGCmight reasonably be expected to look like, if itwere to be developed.

3.8. Approximations of the Carrier-Greenspanperiodic solution to the shallow water waveequations for flows on a sloping beach

Sudi Mungkasi (Australian National University)

16:30 Mon 26 September 2011 – 24.G01

Sudi Mungkasi and Stephen Gwyn Roberts

The Carrier-Greenspan solutions to the shallowwater wave equations for flows on a sloping beachare of two types, periodic and transient. This talkfocuses only on periodic-type waves. We review anexact solution over the whole domain presented byJohns [Numerical integration of the shallow wa-ter equations over a sloping shelf, InternationalJournal for Numerical Methods in Fluids, 2(3):253–261, 1982] and its approximate solution (theJohns prescription) prescribed at the zero point ofthe spatial domain. A new simple formula for theshoreline velocity is presented. We also presentnew higher order approximations of the Carrier-Greenspan solution at the zero point of the spa-tial domain. Furthermore, we compare numericalsolutions obtained using a finite volume methodto simulate the periodic waves generated by theJohns prescription with those found using thesame method to simulate the periodic waves gen-erated by the Carrier-Greenspan exact prescrip-tion and with those found using the same methodto simulate the periodic waves generated by thenew approximations. We find that the Johns pre-scription may lead to a large error. In contrast,the new approximations presented in this talk pro-duce a significantly smaller error. This talk is apresentation of our recently published work in theInternational Journal for Numerical Methods inFluids (http://dx.doi.org/10.1002/fld.2607).

3.9. On the fixed points of computable functions

Petrus H Potgieter (University of South Africa)


Petrus H Potgieter

The Brouwer fixed-point theorem has been shownto be essentially non-constructive and non-computable.The counter-examples of Orevkov and Baigger im-ply that there is no procedure for finding the fixedpoint in general by providing an example of a com-putable function (in the sense of the Polish schoolof computable analysis) which does not fix anycomputable point. This talk takes a closer look athow non-computable points appear in the sets offixed points of computable functions on the unitsquare.

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4.1. Turing patterns and subcellular proteinlocalisation

Christopher Angstmann (University of New South

Wales)

15:00 Mon 26 September 2011 – 24.G02

Christopher Angstmann

In his seminal 1952 paper Turing proposed areaction-diffusion mechanism to explain morpho-genesis. The same mechanism appears to be re-sponsible for some aspects of subcellular proteinlocalisation in bacteria and archaea. In particu-lar the position of the septum in cell division isbased on a Turing pattern. Spectral decompo-sition of the linearised form of a general set ofreaction-diffusion equations allows us to predictthe location of the septum without knowing theunderlying proteins involved, or their dynamics.The location of the septum is then based only onthe shape of the cell.

4.2. On exact solutions of integrable discreteequations

James Atkinson (University of Sydney)

11:30 Thursday 29 September 2011 – 24.G02

James Atkinson

Consider the famous multi-soliton solutions of theKorteweg de-Vries equation first written in ex-plicit form by Hirota. Besides their physical sig-nificance, such solutions are now known to capturethe mathematical heart of this integrable non-linear system. In fact all important features arepreserved when not the solitons them-selves, buttheir characteristic feature of non-linear superpo-sition principle becomes the central object. Moregeneral systems of this kind have been discoveredand in fact now classification results exist withincertain natural restricted classes of such objects.I will cover aspects of this story with a focus onrecently discovered exact solutions and the im-portant system discovered by V.E.Adler known asQ4.

4.3. Multidimensional Discrete Inverse Scattering

Samuel Butler (University of Sydney)

16:30 Mon 26 September 2011 – 24.105

Samuel Butler

A multidimensional inverse scattering transformfor partial difference equations of two independentvariables is presented. The equations consideredpossess a 3D consistency property, and give a vari-ety of well-known partial integrable partial differ-ential equations in various continuum limits, suchas the KdV equation. The defining features of this

IST are discussed, as are multidimensional solu-tions to this hierarchy of integrable lattice equa-tions.

4.4. Model for carbon nanocones

Barry Cox (University of Adelaide)

12:30 Wednesday 28 September 2011 – 24.G02

B.J. Cox and J.M. Hill

Carbon nanocones may be considered a sheet ofgraphene with a section removed which is thenjoined to form a conical nanostructure. Closednanocones may have one of five conical angleswhich are determined by the amount of thegraphene sheet that is missing and this in turn de-termines the number of pentagonal rings requiredto close the apex of the cone. In previous studiesof the structure of nanocones there has been greatinterest on the structure and morphology of theapex for various cone angles. However in the mod-eling presented here we concentrate on accountingfor the curvature effects relevant along the wall ofthe nanocone, both close to and further away fromthe conical apex. We derive an analytical expres-sion for the cone radius for any distance alongthe cone wall and also an integral expression fora correction to the conical height, which go someway towards accounting for the varying curvatureof the cone wall. The predictions of this modelare compared to molecular simulation results per-formed by the authors using LAMMPS.

4.5. Finite-time singularities in the boundary-layerequations: the fluid filled torus

Jim Denier (University of Adelaide)


Jim Denier

This talk will present results on a study of the flowwithin a fluid filled torus. Such a flow providesa paradigm for the study of unsteady boundary-layer separation, transition to turbulence in tran-sient flows and the importance of decaying turbu-lence upon the dynamics of rotating flows. Thistalk will mainly focus upon the finite time singu-larities that arise in the boundary layer that isgenerated on the torus wall when the flow is spunup from rest (or alternatively spun down from astate of rigid body rotation). The effect of thesingularity will be described, and if time permitsthe subsequent singularities of the flow will alsobe considered.

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4.6. The acquisition of genetic pathways inbacteria

Andrew Francis (University of Western Sydney)

15:30 Mon 26 September 2011 – 24.G02

Andrew Francis

4.7. Liouville theorem for some infinite-dimensionaldiffusions

Ben Goldys (University of New South Wales)


Ben Goldys

We will show that the Liouville Theorem holdsfor generators of some stochastic partial differen-tial equations. This result will be applied to theanalysis of long-time behaviour of solutions.

4.8. Fokker-Planck equations for anomaloussubdiffusion in space-and-time-dependent forcefields

Bruce Henry (University of New South Wales)


C. Angstmann, B.I. Henry, T.A.M. Langlands, P.

Straka

The Fokker-Planck equation models the evolutionof the probability density function for diffusion ina force field. It unifies and generalizes Einstein’stheory of Brownian motion, Bachelier’s theory ofrandom walks and Langevin’s theory of stochas-tic dynamics. Applications, which range acrossalmost all areas of science, include the dispersalof pollutants in fluids and the pricing of deriva-tives in financial markets. A central aspect of thediffusion modelled by the Fokker-Planck equationis that the mean square displacement of diffusingentities scales linearly with time.

Over the past few decades sophisticated exper-iments and data collection in numerous biologi-cal, physical and financial systems have revealedanomalous subdiffusion in which the mean squaredisplacement grows slower than linearly with time.A major theoretical challenge has been to obtainthe appropriate revised Fokker-Planck equationfor modelling such anomalous subdiffusion in aspace-and-time-dependent force field.

We have derived Fokker-Planck equations for thispurpose. Our derivations are based on the physi-cally consistent theory of biased continuous timerandom walks, using mathematical tools fromfractional calculus and stochastic calculus.

4.9. Painleve II Asymptotics

Philip Howes (University of Sydney)

16:00 Mon 26 September 2011 – 24.105

P Howes

Some results of the asymptotics of the second con-tinuous Painleve equation are given. The results

involve the explicit knowledge of Okamotos spaceof inital conditions (the regularisation of the vec-tor field) for the equation.

4.10. The repellor and the limit set in complexdynamics of the Painleve equations

Nalini Joshi (University of Sydney)


Nalini Joshi

The asymptotic behaviours of the solutions of thePainleve equations can be analysed in their spaceof initial values, which is a non-autonomous ver-sion of phase space. I show how to construct andunderstand their repellors and limit sets in thisspace.

4.11. Role of regulatory T cells in producing arobust immune response and maintainingimmunodominance

Peter Kim (University of Sydney)

16:00 Mon 26 September 2011 – 24.G02

Peter Kim, Peter Lee, Doron Levy

Several theories exist concerning primary T cellresponses, the most prevalent being that T cellsfollow developmental programs. We propose thealternative hypothesis that the response is gov-erned by a feedback loop between conventionaland adaptive regulatory T cells (iTregs). By de-veloping a mathematical model, we show that theregulated response is robust to a variety of pa-rameters and propose that T cell responses maybe governed by emergent group dynamics ratherthan by autonomous programs.

We extend this model to show how T cell regu-lation may apply to immunodominance. Immun-odominance refers to the phenomenon in which si-multaneous T cell responses organize themselvesinto clear hierarchies. We extend our model ofT cell regulation to consider multiple, concurrentT cell responses. Using our model, we show thatiTreg-mediated regulation leads to a hierarchicalexpansion of T cell responses as observed in thephenomenon of immunodominance.

4.12. Stability and Instability in Kink-waveSolutions to the Sine-Gordon Equation

Robert Marangell (University of Sydney)


R. Marangell and C. K. R. T. Jones

This talk investigates the spectrum of the lin-ear operator coming from the sine-Gordon equa-tion linearized about a traveling kink-wave solu-tion. Using various geometric techniques as wellas some elementary methods from ODE theory, itis shown that the point spectrum of such an oper-ator is purely imaginary provided the wave speedc of the traveling wave is not ±1. Instabilities

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must therefore be due to the presence of essentialspectrum in the right half plane. By calculatingthe essential spectrum it is shown that the trav-eling wave is stable when the quantity c2 − 1 isnegative and unstable when c2 − 1 is positive.

4.13. How long does it take to compute theeigenvalues of a random matrix

Govind Menon (Brown University)


Percy Deift, Govind Menon, Christian Pfrang

The symmetric eigenvalue algorithm is of fun-damental importance in applied mathematics.We present the results of an extensive empiricalstudy of three eigenvalue algorithms (QR, Toda,signum) on matrices chosen at random from a va-riety of ensembles. The main finding is a form ofuniversality for the runtime distribution.

The methods of integrable systems make two ap-pearances: (i) in the integrable structure of thealgorithms; (ii) in the ‘integrable’ structure of ran-dom matrix theory.

No background in integrable systems, random ma-trix theory, or numerical analysis will be presumed(though of course it would help!)

4.14. Transient heat transfer in longitudinal fins ofvarious profiles with temperature-dependentthermal conductivity and heat transfer coefficient

Joel Moitsheki (University of the Witwatersrand)


R.J. Moitsheki and C. Harley

Transient heat transfer through a longitudinal finof various profiles is studied. The thermal conduc-tivity and heat transfer coefficient are assumed tobe temperature dependent. The resulting partialdifferential equation is highly nonlinear. ClassicalLie point symmetry methods are employed andsome reductions are performed. Since the govern-ing boundary value problem is not invariant underany point symmetry , we therefore solve the orig-inal partial differetial equation numerically. Theeffects of the realistic fin parameters such as thethermo-geometric fin parameter and the exponentof the heat transfer coefficient on the temperaturedistribution are studied.

4.15. In silico investigation of clonal dynamics inthe epidermis: simulating the Single Progenitor Cellmodel.

Graeme Pettet (Queensland University of

Technology)

16:30 Mon 26 September 2011 – 24.G02

Beth Addison-Smith and Graeme J. Pettet

Recent measurements of clone size in the basallayer of the murine inter-follicular epidermis have

raised questions about long–held theoretical mod-els of keratinocyte colony structure in the basallayer of the epidermis. These measurements ledto the proposal of a novel theory of keratinocytemitosis and differentiation in the epidermal basallayer. We have translated this theoretical modelinto cellular automata in an attempt to reproducethe measured clone-size dynamics. Our simula-tions raise a number of interesting questions aboutthe theoretical model, and we propose a simplenew model that addresses some of these concerns.

4.16. Stochastic self-similar solutions emerge fromstochastic reaction-diffusion equation

Tony Roberts (University of Adelaide)


A. J. Roberts and Wei Wang

Similarity solutions have an important role inmany applications—stochastic similarity shouldalso be important. Here we explore a class of sto-chastic reaction, advection, diffusion pdes. Bytransforming to log-time, Wayne’s transforma-tion, algebraic decay of diffusion transforms toexponential attraction of the Gaussian similar-ity solution. A stochastic slow manifold modelis then constructed for dynamics perturbed bysmall advection, reaction and stochastic forcing.The stochastic slow manifold evolution describesthe emergent long time dynamics. This approachadapts to the case of dispersion in a stochasticshear flow—a case which is physically interestingas relevant to turbulent dispersion.

4.17. Mathematical modelling of image convertersand intensifiers

Alla Shymanska (Auckland University of

Technology)

15:30 Mon 26 September 2011 – 24.105

Alla Shymanska

This work is devoted to numerical developmentof image converters and intensifiers which in-corporate an inverting electron optical system(EOS)and a microchannel plate (MCP) as an am-plifier. The use of MCP requires the image planeto be flat to match the channel plate, and theplate position should be coincide with the surfaceof the best focusing. Parameters of the systemshould be chosen to minimize a noise factor of theMCP which affects the visual acuity of an imag-ing device . Moreover, some image distortions, asa result of transferring the image from the pho-tocathode to the screen by EOS, should be mini-mized. The numerical design of the system, whichsatisfies such requirements and provides high res-olution, includes calculations of the electrostaticfield in the device, trajectories of electrons emittedfrom a photocathode, and determination of themodulation-transfer-function (MTF) which gives

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the objective estimation for the image quality.Calculations of the potential distribution insidethe device are based on the finite-difference ap-proximation of the Laplace equation. The electrontrajectories are calculated using the Runge-Kuttamethod. The MTFs are obtained using the tra-jectories of the electrons, and the electron densityfunction calculated here. Results of the numericalexperiments are shown, and the EOS with opti-mized characteristics is developed.

4.18. Almost-invariant sets in open dynamicalsystems

Robyn Stuart (University of New South Wales)

17:00 Mon 26 September 2011 – 24.105

Robyn Stuart

We explore the concept of metastability or almost-invariance in open dynamical systems. In suchsystems, the loss of mass through a “hole” occursin the presence of metastability. We extend exist-ing techniques for finding almost-invariant sets inclosed systems to open systems by introducing aclosing operation that has a small impact on thesystem’s metastability.

4.19. Modeling encapsulation of acetylenemolecules into carbon nanotubes

Ngamta Thamwattana (University of Wollongong)


Ngamta Thamwattana

Polyacetylene is a well-known conductive polymerand when doped its conductivity can be alteredby up to 12 orders of magnitude. However, dueto entropy effects a polyacetylene chain usuallysuffers from distortions and interchain couplingswhich lead to unpredictable changes in its con-ducting property. Encapsulating a polyacetylenechain into a carbon nanotube can resolve these is-sues. Furthermore, since the carbon nanotube it-self possesses excellent electrical conductivity, thecombination of the carbon nanotube and poly-acetylene may give rise to a new material with su-perior transport behavior. Here, we model math-ematically the molecular interaction between anacetylene molecule and a carbon nanotube in or-der to determine conditions at which configura-tions of the acetylene molecule are accepted intothe carbon nanotube as well as its equilibriumconfigurations inside various sizes of carbon nan-otubes. For special cases of the acetylene moleculelying on the tube axis, standing vertically with itscenter on the tube axis and staying far inside thetube, explicit analytical expressions for the inter-action energy are obtained.

4.20. Complete integrability of mappings obtainedfrom the discrete Kortegweg-De Vries and a doublecopy of the discrete potential Kortegweg-De Vriesequations

Thi Dinh Tran (University of New South Wales)


Thi Dinh Tran

We study the complete integrability of mappingsobtained as (N,−1)-reductions of the discreteKortegweg-De Vries equation and a double copyof the discrete potential Kortegweg-De Vries equa-tion. We show that the mapping associated withthe double copy of the pKdV equation is super in-tegrable. The mapping corresponding to the KdVequation which can be derived from the previousmapping is completely integrable.

4.21. General Model for Molecular Interactions ina Benzene Dimer

Thien Tran-Duc (University of Wollongong)


Thien Tran-Duc, Ngamta Thamwattana, Barry J.

Cox, James M. Hill

Modelling molecular interactions in a benzenedimer is a typical example of a class of problemsinvolving aromatic molecules. Although manystudies on the benzene dimer have been carriedout both theoretically and experimentally and en-ergetically favorable structures of a benzene dimerhave been found, an investigation of all equilib-rium structures of a benzene dimer has not so farbeen done. Here, we apply an approach in whichthe discrete atomic structure of a benzene mole-cule is replaced by two continuous rings of atoms,namely an inner carbon ring and an outer hydro-gen ring with average constant atomic densitiesand the molecular interaction forces are calculatedfrom the Lennard-Jones potential function. Ananalytical expression for the interaction energy isobtained which we use to determine all equilib-rium structures of a benzene dimer as well as todetermine those domains in which certain config-urations are more favorable than others. Our re-sults show that parallel, T-shaped, parallel dis-placed and tilted structures are all possible con-figurations of a benzene dimer and they exist atdifferent regions of vertical and offset distances atdifferent energy levels.

4.22. Infiltration in the Green-Ampt limit.

Dimetre Triadis (La Trobe University)


Dimetre Triadis

Behaviour for vertical infiltration as the diffusivityapproaches a delta function has been the cause fordebate and subject to some uncertainty. Recent

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progress with an analytic nonlinear model has pro-vided the exact infiltration coefficients for realisticsoil behaviours with non-singular hydraulic func-tions, as well as their exact delta function diffu-sivity limits.

For a realistic soil, the well known Green-Ampt in-filtration function is only obtained as an extremelimiting case where the diffusivity approaches adelta function much faster than the conductiv-ity approaches a step function. Better agreementwith experiment is obtained from a limiting delta-function diffusivity with a matching Gardner ex-ponential hydraulic conductivity function. Sev-eral new soil models presented demonstrate thatvalues of the second Philip infiltration coefficientdiffering from the Gardner model are possible forrealistic limiting step function conductivities. Themodels also show that in the delta function diffu-sivity limit, the solution behaves as if the potentialat the wet front were time-dependent, decreasingin magnitude from an initial value at the tradi-tional Green-Ampt level.

4.23. Understanding Anomalous Delays in Modelsof Intracellular Calcium Dynamics

Martin Wechselberger (University of Sydney)

17:00 Mon 26 September 2011 – 24.G02

Emily Harvey, Vivien Kirk, Hinke Osinga, James

Sneyd and Martin Wechselberger

In many cell types, oscillations in the concentra-tion of free intracellular calcium ions are usedto control a variety of cellular functions. It isthus important to understand the mechanisms un-derlying the generation and control of such pat-terns. We use geometric singular perturbationtechniques to study the dynamics of representa-tive calcium models. In particular, we show howrecently developed canard theory for singularlyperturbed systems with three or more slow vari-ables applies to these calcium models. More pre-cisely, the presence of a curve of folded singu-larities and corresponding canards can result inanomalous delays in the response of these mod-els to a pulse of inositol (1,4,5)-trisphosphate(IP3) which is another important intracellular sec-ondary messenger.

4.24. Stability and bifurcation analysis of amathematical model for gene expression

Tonghua Zhang (Swinburne University of

Technology)

15:00 Mon 26 September 2011 – 24.105

T. H. Zhang and Y. L. Song

Oscillation is a commonly encountered nonlinearphenomenon in biological problem, especially forprocesses with a time delay. It could result inunstable equilibrium or Hopf bifurcation. In this

paper, we consider a mathematical model describ-ing the process of gene expression. Using timedelay as a parameter, we investigate the stabil-ity of the equilibrium. The critical value of thetime delay is also found, which agrees well withthe known result and the experimental data aswell. At the critical value of the time delay, Hopfbifurcation and its bifurcation direction are stud-ied, which are based on the normal form theoryfor delayed differential equation. The effect of theparameters, such as the Hill coefficient, referenceconcentration of protein and degradation rates onthe bifurcation direction is also discussed.

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5.1. On some simple and purely infiniteExel-Larsen crossed product C∗-algebras

Nathan Brownlowe (University of Wollongong)


Nathan Brownlowe, Astrid an Huef, Marcelo Laca,

Iain Raeburn

We will look at some simple and purely infiniteExel-Larsen crossed product C∗-algebras associ-ated to compact abelian groups.

5.2. Entropy of shifts on topological graphC∗-algebras

Valentin Deaconu (University of Nevada, Reno)


Valentin Deaconu

We give entropy estimates for two canonical noncommutative shifts

Φ : C∗(E)→ C∗(E) and Ψ : FE → FEon the C∗-algebra and core algebra of some topo-logical graphs, defined using a basis of the C∗-correspondence H(E). We compare their topolog-ical entropies as unital completely positive mapswith the loop and block entropies that we asso-ciate directly to the topological graph. We showthat the entropies of Φ |FE

and Ψ are differentin general. We illustrate with some examples oftopological graphs where the vertex and the edgespaces are unions of unit circles.

5.3. Co-universal C∗-algebras associated withaperiodic k-graphs

Sooran Kang (University of Wollongong)


Sooran Kang

For a row-finite k-graph Λ, C∗min(Λ) is called theco-universal C∗-algebra if given any C∗-algebra Bgenerated by a Toeplitz-Cuntz-Krieger Λ-familyin which all the vertex projections are nonzero,there is a canonical homomorphism from B ontoC∗min(Λ). The co-universal property naturallyarises in the description of the gauge-invariantuniqueness property and it has been used to de-scribe the ideal structure of certain C∗-algebrasassociated with topological graphs. In this talk,we describe how to construct the co-universal C∗-algebras associated with row-finite aperiodic k-graphs using the boundary path space. This isjoint work with Aidan Sims of the University ofWollongong, Australia.

5.4. Cohomology of higher rank graphs

Alexander Kumjian (University of

Wollongong/University of Nevada, Reno)


Alexander Kumjian, David Pask and Aidan Sims

We introduce a homology theory and the cor-responding cohomology theory of a higher rankgraph (inspired by the cubical homology whichappears in Massey’s text). We also define theC∗-algebra of a k-graph twisted by a two-cocyclewhich takes values in the circle and derive somebasic properties. Interim report on joint workwith David Pask and Aidan Sims.

5.5. A new perspective on topological graphalgebras

Hui Li (University of Wollongong)


Hui Li, David Pask and Aidan Sims

Katsura posed the notion of topological graphswhich includes the directed graphs. He also de-fined a type of C∗-algebras OX by taking the quo-tient of the Toeplitz algebras associated to thetopological graphs. Specifically, when the topo-logical graph is a directed graph, then the Cuntz-Pimsner algebra coincides with the C∗-algebragenerated by the directed graph. In this talk,we are going to find a easy way to describe theToeplitz representations and covariant Toeplitzrepresentations without invoking the Hilbert mod-ules material but only by writing down the alge-braic relations between the functions.

5.6. Twisted K-theory and bivariant Chern–Connestype character of some infinite dimensional spaces

Snigdhayan Mahanta (The University of Adelaide)


Snigdhayan Mahanta

I will outline the construction of a bivariant K-theory in a general operator algebraic frame-work following Cuntz for studying the twisted K-theory and K-homology of some infinite dimen-sional spaces like SU(∞). I will also construct abivariant Chern-Connes type character taking val-ues in Puschnigg’s bivariant local cyclic homology.I will analyse the dual (twisted) K-homologicalunivariant Chern-Connes type character in detail.

5.7. Actions of Ore Semigroups on Higher Rankgraphs

Ben Maloney (University of Wollongong)


Ben Maloney

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An elegant theorem of Kumjian and Pask saysthat if a group G acts freely on a directed graphE, then the associated crossed product C∗(E)oGof the graph algebra is stably isomorphic to thegraph algebra C∗(G\E) of the quotient graph.Their theorem has been extended in several direc-tions: to actions of groups on higher-rank graphs,by Kumjian and Pask, and Pask, Quigg and Rae-burn, and to actions of Ore semigroups on directedgraphs, by Pask, Raeburn and Yeend (PRY). Wewish to consider actions of Ore semigroups onhigher-rank graphs.

Our main theorem directly extends that of PRYto higher-rank graphs, with some interesting newfeatures. First of these is our more efficientuse of Laca’s dilation theory for endomorphic ac-tions: by exploiting his uniqueness theorem, wehave been able to avoid the complicated direct-limit constructions used in PRY. Second, we havefound an explicit isomorphism, which led us torevisit the case of group actions. A third fea-ture of general interest is our direct approachto crossed products of the C∗-algebras of skew-product graphs, which is based on the treat-ment of skew products of directed graphs inKaliszewski, Quigg and Raeburn.

5.8. Dimension in noncommutative geometry

Adam Rennie (Australian National University)


A. Rennie, R. Senior

I will discuss the role that dimension plays in de-termining when a ‘space’, classical or noncommu-tative, is geometric.

5.9. Equivalence and amenability for Fell bundles

Aidan Sims (University of Wollongong)


Aidan Sims and Dana P. Williams

I will report on current joint work with DanaWilliams of Dartmouth College. I will first out-line an elegant proof that the Muhly-Williams im-primitivity bimodule X for the full C∗-algebras ofequivalent groupoids is an off-diagonal corner ofthe full C∗-algebra of a linking bundle, and thatthe quotient map to the reduced algebra of thelinking bundle carries X to an imprimitivity bi-module for the reduced C∗-algeras. I will thendiscuss how to use this result to see that if B is aFell bundle over a groupoid G such that the orbitspace of G is a T0 topological space and the re-striction of B to each isotropy group is metricallyamenable in the sense that its full and reducedC∗-algebras coincide, then the full and reducedC∗-algebras of B coincide also.

5.10. k-coloured graphs and k-graphs.

Samuel Webster (University of Wollongong)


Robert Hazlewood, Iain Raeburn, Aidan Sims and

Samuel B.G. Webster

We provide a concrete description of the relation-ship between k-coloured graphs and k-graphs, andprove some results about the topology of the pathspace, and simplicity of the associated C*-algebra.

5.11. Spectral Triples for Hyperbolic DynamicalSystems

Michael Whittaker (University of Wollongong)


Michael Whittaker

In this talk I will define spectral triples on hyper-bolic dynamical systems known as Smale spaces.The summability of one of these spectral triplesis shown to recover the topological entropy of theSmale space itself.

I will give an introduction to Smale Spaces andtheir associated C∗-algebras. I plan to concen-trate on a specific example and no backgroundin dynamics is necessary. Spectral triples will beintroduced along with some accompanying defi-nitions and examples. Finally, a type of metricon equivalence classes of a Smale space is defined,which gives rise to spectral triples.

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6. Optimisation

6.1. Lipschitzian properties of Newton’s iteration

Francisco Javier Aragon Artacho (The University

of Newcastle)


F. J. Aragon Artacho, A. L. Dontchev, M. Gaydu,

M. H. Geoffroy, and V. M. Veliov

For a version of Newton’s method applied to ageneralized equation with a parameter, we extendthe paradigm of the Lyusternik-Graves theoremto the framework of a mapping acting from thepair “parameter-starting point” to the set of cor-responding convergent Newton’s sequences. Un-der ample parameterization, the Lipschitz-like (orAubin) property of the mapping associated withconvergent Newton’s sequences becomes equiva-lent to the metric regularity of the mapping asso-ciated with the generalized equation.

6.2. Lagrangian decomposition: a hierarchy ofdecompositions and computational trade-offs

Natashia Boland (The University of Newcastle)


Natashia Boland and Olivia Smith

Lagrangian relaxation and Lagrangian duality arepowerful tools in solving mixed integer program-ming problems, both in terms of finding high-quality feasible solutions and finding good dualbounds for proving optimality of solutions. How-ever these tools are predicated on a decomposi-tion of the problem which splits the constraintsinto two sets. Many applications, such as con-strained shortest path problems arising in meth-ods for crew and vehicle scheduling, do not lendthemselves to this decomposition structure. Anapproach known as Lagrangian decomposition of-fers an alternative, exploiting natural partitions ofthe constraints into multiple sets. This approachhas attractive theoretical properties, but has notbeen as widely explored in the literature as stan-dard Lagrangian relaxation, perhaps because ittends to produce a dual space of very high dimen-sion. Here we show that it is possible to constructa hierarchy of alternative Lagrangian decmoposi-tions which trade off the dimension of the dualspace (and hence computational difficulty of com-puting a dual bound) against the quality of thebound obtained. We illustrate these ideas usingconstrainted shortest path problems with multipleside constraints.

6.3. Some Algorithms in Revealed PreferenceTheory

Andrew Craig Eberhard (Royal Melbourne

Institute of Technology)


Andrew Craig Eberhard (other authors D. Ralph, L.

Stojkov and J-P Crouzeix)

When dealing with consumer demand in economicmodeling, researchers often solve the optimiza-tion problem which maximises utility for a givenbudget constraint. Commonly used utilities areCobb–Douglas and CES functions In practise wedo not have access to the utility but only have ac-cess to a finite selection of demand data that as-signs a consumers choice of a commodity bundleto a given price. This data is sometimes contra-dictory and often not of high quality.

The problem of fitting a utility function to thisfinite data set which yields the same preferencestructure was first solved by Afriat and recentlythere have been proposed other approaches by au-thors such as Crouzeix. We discuss some numer-ical algorithms and techniques to perform theseapproximations and how one can accomodate de-viations from the standard model of consistentconsumer preference. A fast heuristic that haspromise of providing a technique for large datasets is discussed. Some philosophical issues ariseas as to what model errors might mean and how toaccommodate them and interpret them. We alsosummarise some recent observation regarding theideal case studies in economic text books.

6.4. Duality and Algorithms for MultiobjectiveLinear Programming

Matthias Ehrgott (The Univesrity of Auckland)


Matthias Ehrgott

Multiobjective linear programming (MOLP) con-cerns the optimization of several conflicting ob-jective functions over a polyhedral feasible set.Solving an MOLP means finding efficient solutionsand corresponding nondominated objective func-tion vectors, which do not allow the simultaneousimprovement of all objectives.

Extensions of the simplex algorithm for MOLPthat work in (possibly high dimensional) vari-able space have been investigated since the 1960s.However, since the number of efficient extremepoints of the feasible set can be very large, thesealgorithms tend to be very slow. In this talkwe consider instead methods which directly workin the (lower dimensional) objective space. We

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6. Optimisation

will first review an improved version of an algo-rithm by Benson that constructs the nondomi-nated set by polyhedral outer approximation. Wethen cover geometric duality, a recently proposedduality theory for MOLP which avoids a dualitygap and where the dual problem is also an MOLP.

We then derive a dual variant of Benson’s algo-rithm that solves the dual problem by outer ap-proximation. Finally, we show that the dual algo-rithm can be interpreted as an inner polyhedralapproximation method for the primal MOLP.

6.5. Turbo-charging the Feasibility Pump

Faramroze Engineer (University of Newcastle)


Natashia L. Boland, Andrew C. Eberhard,

Faramroze G. Engineer, Matteo Fischetti, and

Martin W.P. Savelsbergh

The Feasibility Pump (FP) has proved to be aneffective method for finding feasible solutions toMixed-Integer Programming (MIP) problems. FPiterates between a rounding procedure and a pro-jection procedure that together provide a sequenceof points alternating between LP-relaxation fea-sible but fractional solutions, and integer but LPinfeasible solutions. The process attempts to min-imise the distance between consecutive iterates,producing an integer feasible solution when clos-ing the distance between them.

Recent advances using constraint propagation demon-strate that enhancements to the rounding pro-cedure aimed at improving LP feasibility of theinteger points can markedly improve the qual-ity of feasible solutions found. Here we explorean alternative idea that generates many integerpoints at each FP iteration. We investigate thebenefits of replacing the rounding procedure witha more sophisticated line search that efficientlyexplores a much larger neighbourhood of integerpoints close to an FP iterate. An extensive com-putational study on 1000+ benchmark instancesdemonstrates the effectiveness of the proposed ap-proach.

6.6. Identifying non-Hamiltonicity of cubic graphsby nested linear programming

Jerzy Filar (Flinders University)


Jerzy Filar, Michael Haythorpe and Seguei

Rossomakhine

Given a cubi graph, we construct a nested se-quence of polyhedral sets containing a, possiblyempty, kernel set H. The latter has the proper-ties that (i) it is defined by polynomially manyconstraints and variables and, (ii) it contains theconvex hull of all Hamiltonian cycles of the graph.

Thus if H is empty, the underlying graph is non-Hamiltonian. The validity of the converse state-ment is an open problem. However, in tests ofhundreds of problems no counterexample has beenencountered to date.

6.7. Sherali-Adams Relaxations of GraphIsomorphism Polytopes

Peter Malkin (BHP Billiton)


Peter N. Malkin

There has been significant interest recently in un-derstanding lift-and-project techniques for con-structing hierarchies of linear programming relax-ations for combinatorial problems. Such lift-and-project procedures have been proposed by Lovaszand Schrijver (1991), Lasserre (2001), Sherali-Adams (1990), among many others. Many com-binatorial problems have been investigated us-ing these methods. We present the Sherali-Adamslift and project hierarchy applied to a graph iso-morphism polytope whose integer points encodethe isomorphisms between two graphs. We es-tablish that Omega(n) iterations are needed inthe worst case before converging to the convexhull of integer points. Moreover, we show thatthe Sherali-Adams relaxations characterize a newvertex classification algorithm for graph isomor-phism, which generalizes the classic vertex clas-sification algorithm and generalizes the work ofTinhofer on polyhedral methods for graph iso-morphism testing. This generalized vertex classi-fication algorithm is also strongly related to thewell-known Weisfeiler-Lehman algorithm, whichsurprisingly can be characterized in terms of theSherali-Adams relaxations of a semi-algebraic set.

6.8. Optimization of connected controlled Markovchains

Boris Miller (Monash University)


Boris Miller

The article considers the optimal stochastic con-trol approach to the analysis of connected con-trolled Matkov chains (CCMC). Models of con-trollable Markov chains (CMC) are appropriateto the analysis of control of flows in the Internet,to the large dams management and many othersareas. The principal difficulty of the application ofCMC is the problem of the models high dimensionparticularly for CCMC. But nowadays this prob-lem is less important due to the development ofmultiprocessor supercomputers that make the nu-merical solution of the optimal control problemsfor CCMC more achievable. Models of CCMCarise in queuing systems with many service lineswhere some idle lines may be used to avoid the

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7. Optimisation

congestion if the principal lines have been sub-jected the huge workload. We suggest the tensorform of the representation for such CCMC andgive the dynamic programming equation in corre-sponding tensor form. Numerical approach to thesolution of the access and service rate control hasbeen proposed.

6.9. Recycling bases in the Halton sequence: anoptimization view

Christopher John Price (University of Canterbury)


CJ Price

A modification of the Halton sequence of quasi-random points is given which allows for the samebase to be used for more than one dimension.The main advantage of this is that the asymptoticuniformity property of Halton sequences becomesrelevant after fewer points than for the originalHalton sequence. A new quality measure usingminimal spanning trees is given, and its connec-tions with global optimization shown. The modi-fied sequence maintains the property that differentpoints differ in each element, which is importantin global optimization for avoiding the projectiondeficiency.

6.10. Alternating projection type algorithms in theabsence of convexity

Brailey Sims (University of Newcastle)


Brailey Sims

6.11. Dynamic Assortment and Pricing underDemand Learning

Masoud Talebian (University of Newcastle)


Natashia Boland, Martin Savelsbergh, Masoud

Talebian

Retailers, from fashion stores to grocery stores,face the common challenge of deciding what rangeof products to offer (assortment planning) and atwhat prices (pricing management). New trendsin business, like mass customization, and entryinto emerging markets, put retailers in situationswhere the size of the market, an important com-ponent of demand, is not exactly known in ad-vance. In this research, we develop a mathemat-ical model to make assortment and pricing deci-sions in situations where the size of the marketis unknown. It incorporates on-line learning us-ing Bayesian updates to establish market size anddynamic programming. Solutions to the modelprovide managerial insights, which can increase aretailer’s efficiency and profitability and can en-able better service.

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7.1. Uniqueness of Morava K-theory.

Vigleik Angeltveit (Australian National University)

15:00 Mon 26 September 2011 – 24.G03

Vigleik Angeltveit

Classical obstruction theory seemingly producesuncountably many A-infinity structures on theMorava K-theory spectrum K(n). We show thatthese A-infinity structures are all equivalent, us-ing a Bousfield-Kan spectral sequence convergingto the homotopy groups of the moduli space ofA-infinity ring spectra equivalent to K(n). Thisspectral sequence has infinitely many differentials,and to show that all the relevant classes die westudy the connective Morava K-theory spectrumk(n) and use the theory of Postnikov towers andS-algebra k-invariants developed by Dugger andShipley.

7.2. Counting lattice points in compactified modulispaces of curves

Norman Do (The University of Melbourne)


Norman Do and Paul Norbury

How many ways are there to obtain a genus gsurface by gluing together the edges of n givenpolygons? For geometric reasons, it is natural togeneralise this problem to the case of stable sur-faces. We show that such an augmented enumer-ation yields lattice point polynomials which canbe recursively computed. Their top degree coef-ficients are intersection numbers on compactifiedmoduli spaces of curves while their constant termsare Euler characteristics of compactified modulispaces of curves. On the other hand, the geo-metric meaning of the intermediate coefficients re-mains a complete mystery. In this talk, we willdefine the lattice point polynomials, present someof their properties, and indicate possible connec-tions to topics such as Gromov-Witten theory andtopological recursion.

7.3. Some remarks on linear elasticity

Michael Eastwood (Australian National University)


Michael Eastwood

I shall present the equations for linearised elas-ticity in three dimensions and explain some linkswith Riemannian and projective geometry.

7.4. On free paratopological groups

Ali Sayed Elfard (University of Wollongong)


Ali Sayed Elfard and Peter Nickolas

Let FP (X) be the free paratopological group ona T1 space X and let i2 be the map of (X⊕X−1⊕e)2 to the subspace FP2(X) of FP (X), whereFP2(X) is the set of all words of reduced lengthnot exceeding 2, X has its original topology andX−1 has the discrete topology. In this talk, wedescribe a base of neighborhoods at the identity ein FP2(X) and give conditions on X under whichthe map i2 a quotient. In addition, we give exam-ples of topological spaces for which i2 is a quotient.

References [1] Elfard, A. S. and Nickolas, P., On the topology of

free paratopological groups, Bulletin of the London Mathematical

Society (Submitted 2010). [2] Fletcher, P. and Lindgren, W. F.,

Quasi-uniform spaces, Lecture Notes in Pure and Applied Mathe-

matics, vol. 77, Marcel Dekker Inn., New York, 1982. [3] Pestov, V.

G., Neighborhoods of the identity in free topological groups, Vestnik

Moskov. Univ. Ser. I Mat. Mekh. (1985), no. 3, 8-10, 101. [4] Ro-

maguers, S., Sanchis, M. and Tkachenko, M., Free paratopological

groups, Proceedings of the 17th Summer Conference on Topology

and its Aplications, vol. 27, 2003, pp. 613-640.

7.5. Topological K-theory

Nora Ganter (The University of Melbourne)


Nora Ganter

This is an expository talk, introducing one of myfavorite tools in algebraic topology. Rather thanfocussing on how exactly K-theory is defined, thetalk aims to give a feel for the enormous successK-theory enjoyed soon after its introduction in thelate 50’s.

7.6. Finite index subgroups of mapping classgroups

Volker Gebhardt (University of Western Sydney)


Jon Berrick, Volker Gebhardt, Luis Paris

The interaction between mapping class groupsand finite groups has long been a topic of inter-est. The famous Hurwitz bound of 1893 statesthat a closed Riemann surface of genus g has anupper bound of 84(g−1) for the order of its finitesubgroups, and Kerckhoff showed that the order offinite cyclic subgroups is bounded above by 4g+2.

The subject of finite index subgroups of mappingclass groups was brought into focus by Grossman’sdiscovery that the mapping class group Mg,n ofan oriented surface Σg,n of genus g with n bound-ary components is residually finite, and thus well-endowed with subgroups of finite index. Thisprompts the “dual” question: What is the min-imum index mi(Mg,n) of a proper subgroup of fi-nite index in Mg,n?

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Results to date have suggested that, like the max-imum finite order question, the minimum indexquestion should have an answer that is linear ing. The best previously published bound due toParis is mi(Mg,n) > 4g + 4 for g ≥ 3. This in-equality is used by Aramayona and Souto to provethat, if g ≥ 6 and g′ ≤ 2g − 1, then any nontriv-ial homomorphism Mg,n →Mg′,n′ is induced byan embedding. It is also an important ingredi-ent in the proof of Zimmermann that, for g = 3and 4, the minimal nontrivial quotient of Mg,0 isSp2g(F2).

I will report on recent work with Jon Berrick andLuis Paris, in which we showed an exact exponen-tial bound for mi(Mg,n). Specifically, we provedthat Mg,n contains a unique subgroup of index2g−1(2g − 1) up to conjugation, a unique sub-group of index 2g−1(2g + 1) up to conjugation,and the other proper subgroups ofMg,n are of in-dex greater than 2g−1(2g + 1). In particular, theminimum index for a proper subgroup of Mg,n is2g−1(2g − 1).

7.7. Oka properties of some hypersurfacecomplements

Alexander Hanysz (University of Adelaide)


Alexander Hanysz

Oka manifolds can be viewed as the “opposite” ofKobayashi hyperbolic manifolds. Kobayashi con-jectured that the complement of a generic alge-braic hypersurface of sufficiently high degree ishyperbolic. Therefore it is natural to ask whetherthe complement is Oka for the case of low de-gree or non-algebraic hypersurfaces. We provide acomplete answer to this question for complementsof hyperplane arrangements, and some results forgraphs of meromorphic functions.

7.8. Deformations of Oka manifolds

Finnur Larusson (University of Adelaide)


Finnur Larusson

The class of Oka manifolds has emerged from themodern theory of the Oka principle, initiated in1989 in a seminal paper of Gromov. They werefirst formally defined by Forstneric in 2009 inthe wake of his result that some dozen possibledefinitions are all equivalent. The Oka propertycan be seen as an answer to the question: whatshould it mean for a complex manifold to be “anti-hyperbolic”? One of the many open problems inOka theory is to clarify the place of Oka mani-folds in the classification theory of compact com-plex manifolds, surfaces in particular. To addressthis problem, we need to understand how the Okaproperty behaves with respect to deformations of

compact complex manifolds. In the talk, we willpresent the first results in this direction.

7.9. Assembly maps and the integral K-theoreticNovikov conjecture

Snigdhayan Mahanta (The University of Adelaide)


Snigdhayan Mahanta

For a countable discrete and torsion free group G,the K-theoretic integral Novikov conjecture withcoefficients in a ring R says that a certain assem-bly map

H∗(BG;KR)→ K∗(R[G])

is (split) injective, where KR denotes the non-connective algebraic K-theory spectrum of R. Iwill show that if such a group is a subgroup ofa general linear group over any field or a sub-group of any almost connected Lie group, thenit satisfies the integral K-theoretic Novikov con-jecture with coefficients in the C∗-algebra of com-pact operators and the algebra of Schatten classoperators. The talk will be based on the preprinthttp://arxiv.org/abs/1107.2191

7.10. Stability of Persistent Homology Invariants

Facundo Memoli (University of Adelaide)


Facundo Memoli

We will describe some results regarding the Gromov-Hausdorff stability of Persistent Homology in-variants arising from Vietoris-Rips simplicial con-structions. These results have applications in thecontext of matching shapes and in data analysis.

7.11. A’Campo curvature bumps

Laurentiu Paunescu (University of Sydney)


Laurentiu Paunescu

In this (joint with T.C. Kuo and S. Koike) workwe will define and describe the distribution of theA’Campo curvature bumps associated to an ana-lytic function in two variables (real or complex)

7.12. Acyclic Embeddings of Open RiemannSurfaces into Elliptic Manifolds

Tyson Ritter (University of Adelaide)


Tyson Ritter

In complex geometry a manifold is Stein if thereare, in a certain sense, ‘many’ holomorphic mapsfrom the manifold into Cn. While this has longbeen well-understood, a fruitful definition of thedual notion has until recently been elusive. In Okatheory, a manifold is Oka if it satisfies a seriesof several equivalent definitions, each stating in

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some way that the manifold has ‘many’ holomor-phic maps into it from Cn. Related to this is thegeometric condition of ellipticity due to Gromov,who effectively showed that it implies a complexmanifold is Oka.

We present recent contributions to three openquestions involving elliptic and Oka manifolds.We show that affine quotients of Cn are ellip-tic, and combine this with an example of Mar-gulis to construct new elliptic manifolds with freefundamental group and vanishing higher homo-topy. It then follows that every open Riemannsurface properly acyclically embeds into an ellip-tic manifold. This extends a previous result foropen Riemann surfaces with abelian fundamentalgroup, and gives a partial answer to a question ofLarusson.

7.13. Triangulations of hyperbolic 3-manifoldsadmitting strict angle structures

Henry Segerman (The University of Melbourne)


Craig D. Hodgson, J. Hyam Rubinstein and Henry

Segerman

It is conjectured that every hyperbolic 3-manifoldwith torus boundary components has a decompo-sition into positive volume ideal hyperbolic tetra-hedra (a “geometric” triangulation of the mani-fold). Under a mild homology assumption on themanifold we construct topological ideal triangula-tions which admit a strict angle structure, whichis a necessary condition for the triangulation to begeometric. In particular, every knot or link com-plement in the 3-sphere has such a triangulation.

7.14. Controlling orbifold topology via the Laplacespectrum

Elizabeth Stanhope (Lewis and Clark College/The

University of Melbourne)


Emily Proctor, Liz Stanhope

We will discuss the degree to which the Laplacespectrum of a Riemannian orbifold determinesthe topology of that orbifold. We will reporton progress in showing that isospectral sets ofRiemannian orbifolds, sharing a lower curvaturebound, contain only finitely many topologicallydistinct orbifolds.

7.15. On JSJ decomposition theorem for Haken3-manifolds

Tharatorn Supasiti (The University of Melbourne)


Tharatorn Supasiti

The Torus Theorem states that if a compact, ori-entable, irreducible 3-manifold admits a singularessential torus, then it either admits an embedded

one or it is a small Siefert fibred space. It is onein a series of beautiful results that explore the in-terplay between algebra and topology. The firstpublished proof was given by Feustel in 1976. Itrelies heavily on the JSJ theory that was devel-oped by Jaco and Shalen, and independently byJohannson. So, in a way, both theories should beviewed together. Here, the existence of a singu-lar essential torus allows us to explicitly constructthe characteristics submanifold K from which thedesired embedded essential torus is contained inits boundary or K is the whole manifold itself.We will give a short proof that uses Aitchison andRubinstein’s short hierarchy.

7.16. Finite and infinite generation of lattices onright-angled buildings

Anne Thomas (University of Sydney)

16:00 Mon 26 September 2011 – 24.G03

Anne Thomas and Kevin Wortman

Examples of right-angled buildings include trees,products of trees, and buildings whose apartmentsare hyperbolic planes tessellated by right-angledpolygons. A lattice on such a building is a groupacting with finite stabilisers so that a certain se-ries converges. We discuss the basic questionof whether lattices on right-angled buildings arefinitely generated. This is joint work with KevinWortman.

7.17. Stringy product on orbifold K-theory

Bryan Wang (Australian National University)

16:30 Mon 26 September 2011 – 24.G03

Bryan Wang

Motivated by orbifold string theory models inphysics, Chen and Ruan discovered a new prod-uct called the stringy product on the cohomologyfor the inertia orbifold of an almost complex orb-ifold. This cohomology with the stringy product isnow called the Chen-Ruan cohomology, as a clas-sical limit of orbifold quantum cohomology the-ory. Later, various versions of stringy product onorbifold K-theory of the inertia orbifold were pro-posed. In recent joint work with Jianxun Hu, wedefine a stringy product on the orbifold K-theoryfor the orbifold itself and show that a modified de-localized Chern character to the Chen-Ruan coho-mology is an isomorphism over the complex coef-ficient. As an application, we find a new producton the equivariant K-theory of a finite group withthe conjugation product, which is different to thewell-known Pontryajin (or fusion) product.

7.18. Twisted Morava K-theory

Craig Westerland (The University of Melbourne)


Hisham Sati and Craig Westerland

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We develop an analogue of twisted K-theory forMorava’s extraordinary K-theories (analogues ofK-theory of vector bundles at higher chromaticlevels). We show that K(n) may be twisted byan (n+2)-dimensional cohomology class; the n=1case recovers a localization of twisted K-theory,and the n=2 case is a restriction of the twistedelliptic cohomology of Ando-Blumberg-Gepner.These theories are equipped with means of com-putation: Atiyah-Hirzebruch spectral sequences,and a Khorami-type theorem.

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8.1. The Fourier-Stieltjes algebra and groupgeometry

Michael Cowling (University of New South Wales)


Michael Cowling and Michael Leinert

The Fourier algebra A(G) is the algebra (un-der pointwise operations) of matrix coefficients ofthe regular representation of a (locally compact)group G. It is an open question whether the al-gebra A(G) determines the group G. We answerthis question for connected Lie groups. The solu-tion uses two facts: an isomorphism from A(G1)to A(G2) determines a homeomorphism betweenthe groups, and this mapping sends cosets (or ob-jects that are nearly cosets) to other objects of thesame kind.

8.2. Boundedness of singular integrals and theircommutators with BMO functions on Hardy spaces.

Xuan Duong (Macquarie University)


The Anh Bui and Xuan Thinh Duong

Let L be a non-negative self-adjoint operator onL(X) where X is a doubling space. In this talk, wewill establish sufficient conditions for a singular in-tegral T to be bounded from certain Hardy spacesHpL (Hardy spaces associated to the operator L) to

Lebesgue spaces Lp, 0 < p ≤ 1, and for the com-mutator of T and a BMO function to be weak-typebounded on Hardy space H1

L. Our results are ap-plicable to the following cases: (i) T is the Riesztransform or a square function associated withthe Laplace-Beltrami operator on a doubling Rie-mannian manifold, (ii) T is the Riesz transformassociated with the magnetic Schrodinger opera-tor on an Euclidean space, and (iii) T = g(L) isthe spectral multiplier of L.

8.3. Higher-dimensional Clifford Fourier transforms

Jeffrey Hogan (University of Newcastle)


Jeffrey Hogan

The Clifford Fourier transform was introduced byBrackx, De Schepper and Sommen in 2005 as theexponential of a Cliffordised Hermite operator.Brackx and De Schepper computed a closed formfor the the kernel of the operator in dimensiond=2. In this talk we describe closed forms for theClifford Fourier kernel and its fractionalisation inall even dimensions and discuss the problem ofcomputing the kernel in odd dimensions. We alsogive results on the covariance properties of theseoperators. This is joint work with Mark Craddock(University of Technology Sydney)

8.4. Quaternic Wavelets

Andrew Morris (University of Newcastle)


Andrew Morris

Quaternionic-valued functions have been used asa model for colour images and Fourier-type trans-forms of such signals have been studied usingvarious Fourier kernels. We develop some ba-sic wavelet theory for quaternionic signals usingthe Fourier kernel which arises from the Clifford-Hermite functions. We present an analog of theconvolution theorem and investigate quadtraturemirror filters. Requirements for the solutionsto dilation equations and the construction of aquaternionic scaling function and multiresolutionanalysis structure are presented. We further dis-cuss design conditions which are required for awavelet basis to be constructed with desired reg-ularity.

8.5. Multi-norms and amenability of groups

Hung Le Pham (Victoria University of Wellington)


H. G. Dales, M. Daws, H. Pham, P. Ramsden

In this talk, I will first discuss the theory of mult-norms which was introduced recently by Dales andPolyakov. This theory will then be used to provesome new characterizations of amenability for lo-cally compact groups. These include a combina-torial condition similar to, but formally weakerthan, Folner’s condition, and also answer the ques-tion of when the module Lp(G) is injective.

8.6. Weighted convolution algebras on locallycompact groups

George Willis (The University of Newcastle)


George Willis

A weighted convolution algebra over a locally com-pact group G is the space

L1w(G) :=

φ ∈ L1

loc(G) | ‖φ‖w =

∫G

|φ(x)|w(x) dx <∞,

where w is a submultiplicative weight, that is, apositive real-valued function satisfying w(xy) ≤w(x)w(y) for every x, y ∈ G. Such weighted con-volution algebras were first studied by Beurlingover abelian groups in relation to the problem ofspectral synthesis, and are now an important classof Banach algebras.

Submultiplicative weights and weighted convolu-tion algebras are generally not difficult to find.This talk describes a specific weighted convolutionalgebra on a totally disconnected, locally compact

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group, G, that is defined in terms of the intrinsicstructure of G. How well Banach algebraic prop-erties of L1

w(G) capture the group structure of Gwill be discussed.

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9.1. Pricing Interest Rate Derivatives in aMultifactor HJM Model with Time DependentVolatility

Carl Chiarella (University of Technology, Sydney)


Ingo Beyna, Carl Chiarella, Boda Kang

We investigate the partial differential equation(PDE) for pricing interest derivatives in the multi-factor Cheyette Model, that involves time-dependentvolatility functions with a special structure. Thehigh dimensional parabolic PDE that results issolved numerically via a modified sparse grid ap-proach, that turns out to be accurate and effi-cient. In addition we study the correspondingMonte Carlo simulation, which is fast since thedistribution of the state variables can be calcu-lated explicitly. The results obtained from bothmethodologies are compared to the analytical so-lution existing for bonds and caplets.

9.2.

Joanna Goard (University of Wollongong)


Joanna Goard

Analytic solutions are found for prices of vari-ance and volatility swaps and VIX options underempirically-validated stochastic volatility modelsfor the dynamics of the underlying assets.

9.3. Multi-Player Dynkin Games

Ivan Guo (University of Sydney)


Ivan Guo

A single period multi-player Dynkin game is con-structed where each player can either exit thegame for a fixed payoff or stay and split the re-maining payoff with the other non-exiting play-ers. The emphasis is put on the rivalrous natureof the payoffs, meaning that the sum of all pay-offs is fixed, but the exact allocation is based onthe players’ decisions. Both pure and mixed strat-egy cases are considered, and an equilibrium con-taining maximin and minimax strategies is con-structed. Furthermore the value at which equi-libria are attained is shown to be unique. Thiswork forms the basis on which multi-player finan-cial game options can be constructed.

9.4. Martingales with given marginals

Kais Hamza (Monash University)


Kais Hamza, Fima Klebaner & Jie Yen Fan

While it is well known that stochastic processesare not uniquely defined by their one-dimensionalmarginals, the question of how to construct mar-tingales with given marginals has recently be-come the focus of a substantial body of work. Inthis talk we will review some of the constructionsfound in the literature.

Joint work with Fima Klebaner and Jie Yen Fan

9.5. Consistent Modeling of SPX and VIXOptions: Efficient Evaluation Issues in Gatheral’sThree-factor Model

Guanghua Lian (Auckland University of

Technology)


Guang-Hua Lian, Robert J. Elliott

It is an important issue to consistently priceoptions written on S&P500 and VIX indices.Gatheral (2007, 2008) proposed a three-factor sto-chastic volatility model to achieve this goal. How-ever, the non-affine structure of the model leads tothe analytical intractability that closed-form pric-ing formula may not exist for S&P500 options, norfor VIX options. Monte Carlo simulation methodadopted in Gatheral is rather inefficient in termsof calculation and model calibration. This studyproposes two analytical asymptotic formulae to ef-ficiently price S&P500 options and VIX options,respectively, based on Gatheral’s three-factor sto-chastic volatility model. By applying singular per-turbation techniques, our formulae are obtainedby solving a set of partial differential equationsystems. We then rigorously justified the con-vergence of the asymptotic formulae. We lastlypresent some numerical examples to demonstratethat our asymptotic formulae can achieve high ef-ficiency and accuracy for a large class of optionswith relative short tenor.

9.6. Calibration of Vasicek and CIR interest ratemodels via generating functions

Marianito Rodrigo (University of Wollongong)


Marianito Rodrigo

We propose a new method to calibrate the Vasicekand CIR interest rate models from bond prices.We define an appropriate generating function andderive recursive relations between the derivativesof the generating function and the bond prices.The parameters of the Vasicek and CIR modelsare then obtained by solving a system of linearlyindependent equations arising from the recursiverelations. We include numerical results that showthe method’s accuracy when bond prices gener-ated from the exact formulas are used. This is

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joint work with R. Mamon of the University ofWestern Ontario.

9.7. Analytically pricing Parisian and Parasianoptions

Song-Ping Zhu (University of Wollongong)


Song-Ping Zhu and Wen-Ting Chen

In this talk, we shall present two analytic solutionsfor the valuation of European- style Parisian andParasian options under the Black-Scholes frame-work. A key feature of our solution procedureis the reduction of a three-dimensional problemto a two- dimensional problem through a coordi-nate transform that has elegantly “absorbed” thedirectional derivative associated with the “barriertime” into the time derivative and thus resulted intwo coupled, but simplifed PDE (partial differen-tial equation) systems. For Parisian options, thecoupled PDE systems are then analytically solvedby applying the Laplace transform technique inconjunction with the construction of “moving win-dow”, which are introduced to evaluate the optionprices backwards, slide by slide, until the valueof the option at a given time and trigger valueis found for a given underlying price. On theother hand, due to the non-resetting mechanismof the Parasian option, the coupled PDE systemsof this type of options are much more compli-cated than those of their Parisian counterparts,and the “moving window” technique fails in thiscase. Alternatively, the double Laplace transformtechnique is then applied to solve for the optionprices in the Laplace space. Of course, our suc-cess of obtaining closed-form analytical solutionin this case hinges on overcoming the difficulty ofanalytically performing Laplace inversions.

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10. Combinatorics

10.1. Computing Bernoulli and Tangent numbers

Richard P Brent (Australian National University)


Richard P Brent and David Harvey

Some algorithms for computing Bernoulli andTangent numbers are described. In particular, wegive a new asymptotically fast algorithm to com-pute the first n Bernoulli or Tangent numbers intime O(S log(n) log(log(n))), where S is the spacerequired to store the output, and hence S is alower bound on the time complexity. We also givea very simple in-place algorithm for computing thefirst n Tangent numbers using O(n2) integer oper-ations. Although this is not asymptotically fast, itis extremely simple and convenient for moderatevalues of n, say up to 1000.

10.2. On quasiprimitive rank 3 permutation groups

Alice Devillers (The University Of Western

Australia)


Alice Devillers, Michael Giudici, Cai Heng Li,

Geoffrey Pearce and Cheryl Praeger

While studying quotients of locally s-distancetransitive groups, we encountered the followingquestion: which multipartite complete graphs Γ =Kn[m] (n ≥ 3) and automorphism group G of Γare such that G acts distance-transitively on Γand the only quotients of Γ by nontrivial normalsubgroups of G are trivial. That implies that G isrank 3 on the set of vertices of Γ and quasiprimi-tive. This led us to look for a classification of rank3 group actions which are quasiprimitive but notprimitive.

Our classification is achieved by first showing thatG must be almost simple and then by classify-ing imprimitive almost simple permutation groupswhich induce a 2-transitive action on a blocksystem and for which a block stabiliser acts 2-transitively on the block. Some of the cases in-volve a detailed study of classical matrix groupsover finite fields.

There are two infinite families and a finite numberof individual imprimitive examples. All examplesbut one involve projective linear groups.

When combined with earlier work of Bannai, Kan-tor, Liebler, Liebeck and Saxl, this yields a classi-fication of all quasiprimitive rank 3 permutationgroups.

This work will be published in the Journal of theLondon Mathematical Society.

10.3. Characterising a family of NeighbourTransitive Codes

Neil Gillespie (The University Of Western

Australia)

16:00 Mon 26 September 2011 – 24.201

Neil Gillespie

We consider codes to be subsets of ordered m-tuples from a fixed alphabet Q of size q, and assuch we interpret codes as subsets of vertices of theHamming graph. An automorphism of the Ham-ming graph, Γ, is a permutation of the vertex setthat preserves adjacency. It is known that Aut(Γ)is isomorphic to the wreath product Sq o Sm, andthat the base group, B, of Aut(Γ) is isomorphicto Smq .

When transmitting a code, C, a single error oc-curs if a single entry in a codeword is changed,and so, in the Hamming graph errors are adjacentvertices to codewords. We define a neighbour of acodeword to be an adjacent vertex of that code-word that is not itself a codeword, and we let C1

denote the set of neighbours of C. We say a codeC is neighbour transitive if there exists an auto-morphism group X ≤ Aut(Γ) such that C and C1

are both X-orbits.

If C is an X-neighbour transitive code with min-imum distance δ ≥ 3, we can show that X has a2-transitive action on Q, and so, following Burn-side’s classical result, is either of almost simple oraffine type. If the action is of almost simple typewe say the code is alphabet almost simple neigh-bour transitive. In this talk we construct someinteresting examples of almost simple neighbourtransitive codes. Using these examples we alsocharacterise alphabet almost simple X-neighbourtransitive codes with δ ≥ 3 and X ∩B 6= 1.

10.4. The Sprague-Grundy function for the realgame Euclid

Bao Ho (La Trobe University)

16:30 Mon 26 September 2011 – 24.201

Nhan Bao Ho

The game Euclid, introduced and named by Coleand Davie, is played with a pair of nonnegative in-tegers. The two players move alternatively, eachsubtracting a positive integer multiple of one ofthe integers from the other integer without mak-ing the result negative. The player who reducesone of the integers to zero wins. Unfortunately,the name Euclid has also been used for a subtlevariation of this game due to Grossman in whichthe game stops when the two entries are equal.For that game, Straffin showed that the losing po-sitions (a, b) with a < b are precisely the same asthose for Cole and Davie’s game. Nevertheless,

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11. Combinatorics

the Sprague-Grundy functions are not the samefor the two games. We give an explicit formulafor the Sprague-Grundy function for the originalgame of Euclid and we explain how the Sprague-Grundy functions of the two games are related.

10.5. Almost regular edge colourings of completebipartite graphs

Barbara Maenhaut (The University of Queensland)


Barbara Maenhaut

A graph G is almost regular on S ⊆ V (G) if thedegrees of any two vertices of S differ by at most1. An edge-colouring of the complete bipartitegraph Km,n is almost regular on S ⊆ V (Km,n)if the spanning subgraph induced by each colouris almost regular on S. In this talk I will illus-trate the proof of the following lemma in whichan edge-colouring of a complete bipartite graph istransformed into an almost regular edge-colouringof that complete bipartite graph.

Lemma Let the vertex set of Km,n be comprisedof the partite sets A and B where |A| = m and|B| = n. Let γ be an edge colouring of Km,n

and let S ⊆ V (Km,n) such that either S ⊆ A orS ⊆ B. Then there exists an edge colouring γ′ ofKm,n such that the following conditions hold:

• For each colour c, the number of edgesof colour c is the same for γ and γ′.• For each x ∈ V (Km,n) \ S and each

colour c, the number of edges of colour cincident with x is the same for γ and γ′.• For x, y ∈ V (Km,n)\S, the colour of the

edge xy is the same for γ and γ′.• The edge colouring γ′ is almost regular

on S.

Applications of this lemma to prove classical re-sults and new results will be presented.

10.6. Recent research in matroid theory

Dillon Mayhew (Victoria University of Wellington)

15:00 Mon 26 September 2011 – 24.201

Dillon Mayhew

A matroid is a geometrical structure that ab-stracts the notion of linear dependence. Therehas been a great deal of recent activity in matroidresearch, and many old conjectures are now withinstriking distance.

This talk will give a brief (and incomplete) overviewof recent matroid research, concentrating on twocontrasting types of results: exact and qualitative.No knowledge of matroid theory will be assumed.

10.7. Normal coverings of finite symmetric andalternating groups

Cheryl Praeger (The University Of Western

Australia)


Cheryl Praeger

A covering of a finite group G is a set of propersubgroups whose union is G. The covering is nor-mal if it is closed under conjugation by G. Theobject is to minimise the number of conjugacyclasses of subgroups involved in a normal cover-ing. Part of our motivation comes from a numbertheoretic application to do with factorisation of in-teger polynomials - and we study the alternatingand symmetric groups as these are the most com-mon Galois groups. We prove that the minimumnumber of conjugacy classes required for a normalcovering of An or Sn lies between aφ(n) and bn forcertain constants a, b, where φ(n) is the Euler phi-function, and we show that the number dependson the arithmetical complexity of n. Moreover weget very tight bounds in the case where n is di-visible by at most two primes. This is joint workwith Daniela Bubboloni [Firenze].

10.8. Higher dimensional Hadamard matrices

Jennifer Seberry (University of Wollongong)


Jennifer Seberry and Tianbing Xia

The Hadamard Conjecture is now over 100 yearsold and still unproven. The conjecture is that a2x2 Hadamard matrix exists for order 1, 2 and4t (t a non-negative integer). We review resultson the status of the conjecture and constructHadamard matrices in higher dimensions whichhave applications in spectroscopy, security, error-correction, signal processing, acoustics and ...

10.9. Disconnected colors in generalized Gallaicolorings

Akos Seress (The University Of Western Australia)


S. Fujita, A. Gyarfas, C. Magnant, A. Seress

Gallai-colorings of complete graphs - edge color-ings such that no triangle is colored with threedistinct colors - occur in various contexts such asthe theory of partially ordered sets (in Gallai’soriginal paper), information theory and the the-ory of perfect graphs. A basic property of Gallai-colorings with at least three colors is that at leastone of the color classes must span a disconnectedgraph. We are interested here in whether this ora similar property remains true if we consider col-orings that do not contain a multicolored copy ofa fixed graph F.

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11.1. Gaussian processes in Hybrid MCMC andSimulated Annealing for computationally expensiveobjective functions.

Mark James Fielding (University of Wollongong)


Mark Fielding, David Nott, S.-Yui. Liong

Hybrid MCMC is considered in Statistical modelswhere evaluating a probability function is compu-tationally expensive, relying on output from a nu-merically intensive computer model. We developefficient methods to minimise the number of func-tion evaluations in MCMC by replacing the tar-get distribution with a Gaussian process approxi-mation. The approximation is used in generatingbetter proposals and the true target is used intheir acceptance/rejection.

Extensions are made to the method of Ras-mussen (2003): Parallel tempering with Ras-mussens scheme, incorporating the true target atall temperatures; Parallel tempering with full re-placement by the approximation at all tempera-tures; And parallel tempering retaining the truetarget only at the lowest temperature. HybridMCMC with the Gaussian process approximationis also considered for efficient Simulated Anneal-ing with a computationally expensive objectivefunction.

11.2. Influence diagnostics for INGARCH timeseries models

Shuangzhe Liu (AMSI)

16:30 Mon 26 September 2011 – 24.101

F. Zhu, S. Liu and P. Xu

In this talk, we consider some INGARCH mod-els to study time series of count data. We re-view the maximum likelihood estimation methodand present gradient vectors, Hessian matricesand other related results. Based on such results,we use case-weights, data and other perturbationschemes to make local influence analysis for someof the models. We include illustrated real dataexamples.

11.3. Statistical Based Arbitrage in FinancialMarkets using Cointegration

Michaael McCrae (AMSI)

15:30 Mon 26 September 2011 – 24.101

M. McCrae, Lin, Y-X, Gulati, C.

This talk reviews the derivation, nature and prop-erties of cointegration - a statistical technique forderiving any stationary relationships among eli-gible I(1) series- especially among financial dataseries. It reviews the application of cointegration

techniques in the financial and derivatives mar-kets through a strategy known as pairs trading.and reviews significant modern developments ofthis technique and its applications.

11.4. Abelian and Tauberian theorems for longmemory random fields

Andriy Olenko (La Trobe University)

15:00 Mon 26 September 2011 – 24.101

A.Olenko

In many cases mathematical models for spatialphenomena or images are obtained as particularexamples of random fields. Models of this typeare often satisfactorily characterized by their cor-relation or spectral functions.

Unfortunately well-known results by Pitman andBingham can not be used to derive asymptoticresults for long-memory random fields. Asymp-totics for the correlation function Bn(r), whenr → ∞ and the isotropic spectral function Φ(λ),when λ→ 0 have been studied. New Abelian andTauberian theorems for some classes of extendedregularly varying functions will be discussed. Var-ious illustrative examples will be given.

11.5. Hybrid Variational Bayes

John Ormerod (University of Sydney)


John Ormerod

Variational Bayesian methods offer computation-ally efficient approaches for fitting many Bayesianmodels. Unfortunately there are models where thequality of these approximations can be quite poor.In this talk a hybrid Variational Bayes/GibbsSampling method will be presented which exploitsthe close connection between the two methods.The resulting method is useful in several con-texts where trading off accuracy for computa-tional speed may be beneficial. Examples illus-trating the approach may include normal mixturemodels, missing data models and bridge regressionmethods, time permitting.

11.6. Approximate Bayesian computation (ABC)and Bayes linear analysis: Towardshigh-dimensional ABC

Scott Sisson (AMSI)


S. A. Sisson, D. J. Nott and Y. Fan

Bayes linear analysis and approximate Bayesiancomputation (ABC) are techniques commonly

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used in the Bayesian analysis of complex mod-els. In this talk we connect these ideas by demon-strating that regression-adjustment ABC algo-rithms produce samples for which first and sec-ond order moment summaries approximate ad-justed expectation and variance for a Bayes lin-ear analysis. This gives regression-adjustmentmethods a useful interpretation and role in ex-ploratory analysis in high-dimensional problems.As a result, we propose a new method for combin-ing high-dimensional, regression-adjustment ABCwith conventional sampler-based approaches (suchas MCMC), thereby providing an improved esti-mate of the joint posterior in high dimensionalanalyses. We illustrate this method with severalexamples, with a focus on predictive inference andmodel checking.

11.7. Gaussian Working Correlation Structure inLongitudinal Data Analysis

You-Gan Wang (University of Queensland)

16:00 Mon 26 September 2011 – 24.101

You-Gan Wang and Vincent Carey

We investigate methods for data-based selection ofworking covariance models in the analysis of corre-lated data with generalized estimating equations.Two selection criteria are studied: Gaussian pseu-dolikelihood, and a geodesic distance based ondiscrepancy between model-sensitive and model-robust regression parameter covariance estima-tors. The Gaussian pseudolikelihood is found tobe reasonably sensitive for several response dis-tributions and non-canonical mean-variance rela-tions for longitudinal data. Assessment of ad-equacy of both correlation and variance modelsfor longitudinal data should be routine in appli-cations, and open source software supporting thispractice is described. Examples are provided us-ing data from two medical studies.

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12. General session

12.1. Hall-Littlewood polynomials andgeneralisations of the Rogers–Ramanujan identities.

Nicholas Bartlett (AMSI)


Nicholas Bartlett

The Hall–Littlewood polynomials are a family ofsymmetric functions which play an important rolein representation theory and algebraic combina-torics. In this talk we will examine their impor-tance in understanding recent work generalisingMacdonald’s eta-function identities and the fa-mous Rogers–Ramanujan identities. We will alsodescribe a new, explicit formula for these poly-nomials, leading to a generalisation of the CnRogers–Selberg identity.

12.2. The Vanishing Art of IntroductoryMathematics

Raymond Booth (Flinders University)


RS Booth / ZA Melzak

This (as yet unpublished) book, authored by Pro-fessor Z A Melzak, retired from the Universityof British Columbia, puts much of undergraduatemathematics in its proper historical perspective.As such much of its material is essential knowledgefor all who teach at first or second year Universitylevel.

12.3. Metric trees of generalized roundness one

Ian Doust (University of New South Wales)


Elena Caffarelli, Ian Doust and Anthony Weston

Every finite metric tree has generalized round-ness strictly greater than one. On the otherhand, some countable metric trees have general-ized roundness precisely one. The purpose of thispaper is to identify some large classes of countablemetric trees that have generalized roundness pre-cisely one. At the outset we consider sphericallysymmetric trees endowed with the usual combi-natorial metric (SSTs). Using a simple geomet-ric argument we show how to determine decentupper bounds on the generalized roundness of fi-nite SSTs that depend only on the downward de-gree sequence of the tree in question. By consid-ering limits it follows that if the downward de-gree sequence (d0, d1, d2...) of a SST (T, ρ) satis-fies |j | dj > 1| = ℵ0, then (T, ρ) has generalizedroundness one. Included among the trees that sat-isfy this condition are all complete n-ary trees ofdepth ∞ (n ≥ 2), all k-regular trees (k ≥ 3) andinductive limits of Cantor trees. The remainderof the paper deals with two classes of countable

metric trees of generalized roundness one whosemembers are not, in general, spherically symmet-ric. The first such class of trees are merely re-quired to spread out at a sufficient rate (with arestriction on the number of leaves) and the sec-ond such class of trees resemble infinite combs.

12.4. Singularly Perturbed Linear ProgrammingProblems

Vladimir Gaitsgory (University of South Australia)


Vladimir Gaitsgory

Some optimization problems are characterized bythe fact that their optimal values my changeabruptly with small changes of data (due to anabrupt change of feasible domains). One of theway of investigating these phenomena is to studyfamilies of problems depending on a parameter insuch a way that the optimal values obtained withsmall positive values of the parameter are signifi-cantly different from those obtained with the zerovalue of the parameter (that is, the dependencesof the optimal values on the parameter are dis-continuous at zero). Such families of optimisationproblems are called singularly perturbed (SP). Inour presentation, we will deal with SP linear pro-gramming problems, and our main focus will beon the construction of the “true limit” problems,the solution of which can be used for constructionof near optimal solutions of the SP problems withsmall but nonzero values of the parameter.

12.5. Nearly Identical Expressions in ExistentialSecond Order Logic for Problems in P and NP

Prabhu Manyem (Shanghai University)


Prabhu Manyem

We consider a problem in finite model theory.We show that a decision problem known to bein the computational complexity class P (Maxi-mum Matching) and another one only known tobe in NP (Maximum Independent Set) have al-most identical expressions in existential second or-der logic. More precisely, the difference is only inthe first order part of the expression, which canbe computed directly from the input structure.The input domain is assumed to have a linear or-der. Thus as far as the second order predicates(the unknowns) are concerned, the expressions areidentical; they are universal Horn formulae.

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13. General session

12.6. A new large cardinal property

Rupert Gordon McCallum (University of New

South Wales)


Rupert McCallum

Reflection principles with a second-order parame-ter yield the large cardinals known as “indescrib-able cardinals”. If one tries to generalise thisin a natural way so as to include parameters ofthird orde or higher, one obtains an inconsistency.Tait in his essay “Constructing Cardinals from Be-low” proposed that this problem could be avoidedby placing restrictions on the formulas to be re-flected. However, some of the reflection principleshe proposed have been proved inconsistent by Pe-ter Koellner in “On Reflection Principles”. Weintroduce a new large-cardinal property which isconsistent relative to an ω-Erdos cardinal whichyields a consistency proof for restricted versionsof these reflection principles.

12.7. p-negative type of finite metric spaces

Stephen James Sanchez (University of New South

Wales)


Stephen Sanchez

The notions of negative type and generalizedroundness have been used extensively in metric ge-ometry to investigate various questions of embed-dability. An early example is Schoenberg’s clas-sical result that a metric space is isometric to asubset of a Euclidean space if and only if it has2-negative type. While the supremal p-negativetype of certain metric spaces such as Lp(µ) andC[0, 1] has been known for some time, calculat-ing the supremal p-negative type of a given finitemetric spaces has remained difficult.

In this talk I will show how by combining resultsof Li and Weston and Wolf, one may calculate thesupremal p-negative type of a given finite metricspace. The result is then applied to calculate thesupremal p-negative types of the complete bipar-tite graphs and to prove a gap in the spectrum ofpossible supremal p-negative type values for pathmetric graphs.

The talk should be accessible to everyone.

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13.1. A non-directed model of polymer adsorption

Nicholas Beaton (MASCOS / University of

Melbourne)


Nicholas Beaton

Self-avoiding walks have long been considered asan idealised model of polymers, and can be usedto study phenomena like polymer collapse and ad-sorption. Thus far the only models which havebeen solved exactly, such as Dyck paths and par-tially directed walks, have a directedness con-straint. I’ll introduce a new model which is notrestricted in this way.

13.2. From second-order to first-order in aninfinite number of steps

Andrea Bedini (MASCOS / University of

Melbourne)


Andrea Bedini

Self-avoiding trails are a model of polymer col-lapse alternative to self-avoiding walks (SAWs)where the paths may revisit sites but not bonds.While it’s established that trails in the swollen(high-temperature) phase are in the same univer-sality class as SAWs, their properties at collapseare not yet fully understood. We present numeri-cal evidence that trails on the simple cubic latticehave, in a larger parameter space, both a first-order and a second-order line of phase transitionswith the two lines meeting at a multi-critical pointof peculiar scaling properties.

13.3. Integrability of BEC/BCS crossoverHamiltonians

Andrew Birrell (University of Queensland)

16:00 Mon 26 September 2011 – 24.202

Andrew Birrell, Jon Links and Phil Isaac

In the last several decades a prolific field of re-search has flourished, dedicated to constructingand analysing exactly solvable quantum models.The understanding of quantum integrability thatmade such analysis tractable finds its origin inthe melding of the Quantum Inverse ScatteringMethod and Bethe Ansatz techniques. This ap-proach can be complicated and difficult to imple-ment. In some instances an ability to extend theexact solutions to the most general Hamiltoniansto which they are applicable is outside the scopeof such techniques. In this talk, I will demon-strate an alternative method, inspired by an oldapproach by Richardson in the 1960s, that enablessuch a determination. In particular we will derivethe integrability conditions for a general family of

BEC/BCS crossover Hamiltonians and determinethe manifolds in the coupling parameter space forwhich they can be solved exactly.

13.4. Current fluctuations in the asymmetricexclusion process

Jan De Gier (The University of Melbourne)

17:00 Mon 26 September 2011 – 24.202

Jan De Gier

I will discuss the current statistics of the one-dimensional asymmetric exclusion process withparticle injection and extraction at two bound-aries. In the limit of infinite system size, I willpresent an exact expression for the current largedeviation function.

13.5. The simplest correction to Hubbell’s law andits theoretical implications

Frank De Silva (AMSI/University of Melbourne)


Frank De Silva

This paper introduces a simple change to theHubbell’s equation on distance to red shift. It isshown that the prediction of the equation is com-patible with data, obtained from distance mea-surements, which are independent of red shift.Having shown its compatibility with these obser-vations, the paper then introduces the theoreticalbasis for the equation. The theoretical basis relieson a single assumption that in the expansion ofthe universe, the ratio d(space)/d(time) = Con-stant = speed of light. It is shown that the equa-tions of special relativity follow directly from this1 assumption.

13.6. Quantum Master Equations from OperatorValued Measures: A Hopf Algebraic Approach

Demosthenes Ellinas (Technical University of

Crete)


Demosthenes Ellinas

Hopf algebras of functions and operators areutilized to develop a mathematical constructionscheme for building generalized diffusion equa-tions, algebraic Markov chains and quantum mas-ter equations, by means of algebraic randomwalks[1-3]. The main construction treats exem-plary cases of elementary Hopf algebras, suchas circle, line, plane, sphere, finite groups andanyonic algebras[4-8]. It studies pairs of covari-ance [9], formed by a translation operator andits associated operator valued measures, such as,OVMs related to Wigner distribution functions

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[10], positive OVM (POVMs) related to posi-tion/momentum distributions of canonical quan-tum systems, and analogous POVMs related todistributions associated to spin quantum systems.The construction utilizes (completely) positivetrace preserving maps (CPTP) of (density) matri-ces [11]. The appropriately defined (weak) asymp-totic limit of the action of such maps, it is shownto lead to quantum master equations of Lindbladtype[12]. Particular quantum master equationsdescribing information loss due to dephasing, arederived and investigated as show cases of openquantum systems [13].

References [1] P. A. Meyer. “Quantum probability for probabilists”.

Lect. Notes Math., Vol.1538, Springer 1993. [2] S. Majid. “Founda-

tions of quantum groups theory”. Cambridge U. Press 1995. [3] U.

Franz and R. Schott. “Stochastic processes and operator calculus on

quantum groups”, Kluwer Acad. Pub. 1999. [4] D. Ellinas. “Quan-

tum diffusions and Appell systems”. J. Comput. Appl. Math., 133,

(2001) 341-353. [5] D. Ellinas and I. Tsohantjis. “Brownian motion

on a smash line”. J. Non. Math. Phys., 8 (Suppl.) (2001)100-105.

[6] D. Ellinas and I.Tsohantjis. “Random Walk and diffusion on

a smash line algebra”. Infin. Dimens. Anal. Quantum Probab.

and Relat. Top., 6, (2003) 245-264. [7] D. Ellinas. “On algebraic

and quantum random walks”, In “Quantum Probability and Infinite

Dim. Analysis: From Foundations to Applications” Eds. M. Schur-

mann and U. Franz, World Sci., Singapore, 2005 p. 174-200. [8] D.

Ellinas. “Hopf algebras, random walks and quantum master equa-

tions”. J. Generalized Lie Theory and Applications. 2 (2008), No.

3, 147–151. [9] P. J. Lahti and J.-P. Pellonpaa. “Covariant phase

observables in quantum mechanics”. J. Math. Phys. 40, (1999)

4688-4698. [10] D. Ellinas and A. J. Bracken. “Phase-space-region

operators and the Wigner function: Geometric constructions and

tomography”. Phys. Rev. A 78, (2008) 052106-052115. [11] V.

Gorini, A. Kossakowski, and E. C. G. Surdasan. “Completely posi-

tive dynamical semigroups of N-level systems”. J. Math. Phys. 17,

(1976) 821-825. [12] G. Lindblad. “On the generators of quantum

dynamics semigroups”. Comm. Math. Phys. 48,(1976)119-130.

[13] H. Breuer and F. Petruccione. “The Theory of Open Quantum

Systems”. 2002 Oxford U. Press.

13.7. Dynamics of the asymmetric exclusionprocess in the reverse bias regime

Caley Finn (The University of Melbourne)

16:30 Mon 26 September 2011 – 24.202

Jan de Gier, Caley Finn, Mark Sorrell

The asymmetric simple exclusion process (ASEP)is a model describing the diffusion of hard-coreparticles along a one-dimensional chain. Withopen boundaries, the ASEP is a non-equilibriumsystem with late time behaviour described by aunique stationary distribution. The relaxationrate to this distribution can be found by solvingthe Bethe ansatz equations for the system. Ear-lier work found the asymptotic behaviour of therelaxation rate in the forward bias regime. We ex-tend these results to the reverse bias regime anddescribe how fine structure in the Bethe ansatzsolutions changes the asymptotic behaviour.

13.8. A Fuchsian differential equation for Selbergcorrelation integrals

Peter Forrester (The University of Melbourne)


Peter Forrester

Certain Selberg correlation integrals are given interms of a basis of solutions of a particular Fuch-sian matrix differential equation. The explicitform of the connection matrix from the Frobe-nius type power series to this basis is calculated.This allows us to determine the leading asymp-totic form of negative moments of the character-istic polynomial, which relates to an effect knownas singularity dominated strong fluctuations.

13.9. Loop models in three dimensions

Timothy Garoni (Monash University)


Timothy Garoni, Youjin Deng, Qingquan Liu

Loop models in two dimensions have been an ac-tive field of study over recent decades, and manyexact results have been found. In three dimen-sions, however, very few results are known. Inthis talk I’ll describe the results of a systematicMonte Carlo study of the O(n) loop model on athree-dimensional 3-regular lattice, for real non-negative n.

13.10. Matrix models, lattice models and anO(N)-Potts correspondence

Alex Lee (The University of Melbourne)


Alex Lee

Matrix models can be used to describe statisticalmechanical models on surfaces of arbitrary Eulercharacteristic. Recently, Eynard and Orantin de-veloped a theory to solve such models and thishas since been used to solve the Ising and O(N)on random surfaces. In this talk I will give a ba-sic introduction to matrix models and outline anapproach to solving the Potts matrix model us-ing a known correspondence with the O(N) matrixmodel.

13.11. Polynomial algebras and superintegrability

Ian Marquette (The University of Queensland)

15:00 Mon 26 September 2011 – 24.202

Ian Marquette

We will present recent results concerning polyno-mial algebras in context of quantum superinte-grable systems. We will discuss superintegrablequantum systems involving the fourth and fifthPainlev transcendents and the generalized MICZ-Kepler system.

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13.12. Integrable Heteroatomic MolecularBose-Einstein Condensates

Eduardo Cerutti Mattei (The University of

Queensland)


Eduardo Cerutti Mattei

We study an exactly solvable model for het-eroatomic molecular Bose-Einstein condensates.We start by revisiting the integrability of themodel through the Yang-Baxter algebra. Usinga classical analysis we determine the phase spacefixed points of the system. It is found that bifur-cations of the fixed points naturally separate thecoupling parameter space in different regions. Re-markably, two distinct scenarios emerge, depend-ing if the number of atoms of different species isequal or not. This result suggests the ground-stateproperties of the model exhibit an unusual sensi-tivity on the atomic imbalance. We then confirmthis finding by a quantum analysis using differentapproaches, such as the energy gap, the fidelity,the entanglement and the behavior of the ground-state solutions of the Bethe ansatz equations.

13.13. A geometric triumvirate of random matrices

Anthony Mays (The University of Melbourne)


Anthony Mays

A random matrix is, broadly speaking, a matrixwith entries randomly chosen from some distri-bution. In the non-random case eigenvalues canoccur anywhere in the complex plane, but, re-markably, random elements imply predictable be-haviour, albeit in a probabilistic sense.

Correlation functions are one measure of a prob-abilistic characterisation and we discuss a 5-partscheme, based upon orthogonal polynomials, tocalculate the eigenvalue correlation functions. Weapply this scheme to three ensembles of randommatrices, each of which can be identified with oneof the surfaces of constant Gaussian curvature:the plane, the sphere and the anti- or pseudo-sphere. We will be using real random matrices,which possess the added complication of having afinite probability of real eigenvalues.

13.14. Integrable Quantum Impurity Models

Amir Moghaddam (The University of Queensland)

15:30 Mon 26 September 2011 – 24.202

Amir Moghaddam, Dr Jon Links and A/Prof.

Yao-Zhong Zhang

We present a new integrable model describingthe interaction of two spin-half impurities in anisotropic Heisenberg chain. Periodic boundaryconditions are imposed on the system. The Hamil-tonian of the new model is obtained based on the

Quantum Inverse Scattering Method and diago-nalised via the algebraic Bethe ansatz.

13.15. The equation of motion of an extendedcharged particle

Andrew Norton (Max Planck Institute for

Gravitational Physics)


Andrew H Norton

If a charged particle is modelled as having an ex-tended charge distribution with finite self-energy,then Maxwell field theory can be used to calcu-late its equation of motion. In this way, one canderive a self-consistent electrodynamics for the ex-tended particle. Conventional wisdom would haveit that this self-consistent electrodynamics shouldnot differ significantly from Maxwell-Lorentz elec-trodynamics. That is, that the equation of mo-tion for the extended charged particle would dif-fer from the Lorentz force equation only by smallradiative corrections and small model-dependentstructure terms. However, a fully relativistic cal-culation for one such particle shows that this con-ventional wisdom is false. The extended parti-cle we consider is a uniformly charged sphere.The self-consistent electrodynamics for this sim-ple particle turns out to be far more interestingthan can be described by any variant of Maxwell-Lorentz theory. It also appears to be a betterphysical description. For example, the spin angu-lar momentum and magnetic moment of the elec-tron can both be modelled within this electrody-namics, and a purely classical explanation can begiven for the failure of Maxwell-Lorentz electrody-namics at the Compton wavelength scale. Theseresults follow directly from Maxwell field theory,so need to be somehow reconciled with quantumtheory.

13.16. Random Tilings of Squares Triangles andRhombi

Maria Tsarenko (The University of Melbourne)


Jan de Gier, Bernard Nienhuis, Maria Tsarenko

In this talk, we introduce an integrable square-triangle-rhombus random tiling model. This modelis an extension of the square-triangle tiling by theaddition of a rhombus. The model is solvable bythe algebraic Bethe Ansatz and the entropy canbe computed in a two-parameter subspace.

Square-triangle-rhombus random tilings are gen-eralisations of rhombus tilings, or non-intersectinglattice paths. Recently it has also been related tothe so called puzzles which compute Littlewood–Richardson coefficients.

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14.1. Fractal transformations associated withBernoulli convolutions

Michael Fielding Barnsley (Australian National

University)


Michael Barnsley

We consider the family of dynamical systems T =T (a, b, ρ) : [0, 1] → [0, 1] where 1 ≤ a + b, 0 <a, b, ρ < 1, T (x) = x/a, 0 ≤ x ≤ ρ, T (x) =x/b+ (1− 1/b) and ρ < x ≤ 1.

Under what conditions on (a, b, ρ) are two suchsystems topologically conjugate? I will outline therich theory of this subject. The material in thistalk is derived from collaboration with B. Hard-ing, K. Igudesman, J. Keesling, N. Mihalache, A.Samuels, N. Singreva and A. Vince.

14.2. Infinitesimal automorphisms of parabolicgeometries and dynamics

Andreas Cap (University of Vienna)


Andreas Cap

14.3. Families of conformal operators along ahypersurface and formal extension problems

Rod Gover (AMSI)

15:00 Mon 26 September 2011 – 24.203

Rod Gover

The problem of constructing conformally invari-ant differential operators along a hypersurface hasbeen looked at by a number of authors in con-nection with the study of Polyakov type formu-lae, conformal Dirichlet-Neumann problems, theasymptotics of Poincare-Einstein manifolds, Q-curvature and the AdS/CFT correspondence ofPhysics. I will discuss recent progress and its con-nection to the asymptotics of a class of conformalboundary problems. This is joint work with LarryPeterson and Andrew Waldron.

14.4. Totally geodesic subalgebras of N-gradedfiliform Lie algebras

Ana Hinic-Galic (La Trobe University)

16:30 Mon 26 September 2011 – 24.203

Grant Cairns, Ana Hinic-Galic, Yury Nikolayevsky

A metric Lie algebra g is a Lie algebra equippedwith an inner product. A subalgebra h of a met-ric Lie algebra g is said to be totally geodesic ifa Lie subgroup corresponding to h is a totally ge-odesic submanifold relative to the left-invariantRiemannian metric on the simply connected Liegroup associated to g defined by the inner prod-uct.

We will start with a brief overview of results ontotally geodesic subalgebras of metric nilpotent(and in particular, filiform) Lie algebras. We willthen give a complete characterisation of the max-imal dimension of totally geodesic subalgebras ofN-graded metric filiform Lie algebras (the ques-tion is motivated by an earlier result of Kerr andPayne).

14.5. Asymptotic Convexity of HypersurfacesMoving by Curvature

Mathew Langford (Australian National University)


Mathew Langford

We study a simple method for obtaining a theoremof Huisken and Sinestrari, which demonstratesthat compact, mean convex, hypersurface solu-tions of the mean curvature flow become (weakly)convex at singular points and see how the proofmight apply to other flows by functions of theprincipal curvatures. The Huisken-Sinestrari re-sult was crucial in classifying singular behaviourof the mean curvature flow.

14.6. Connected irreducible subgroups of O(2,n)

Thomas Leistner (University of Adelaide)


Thomas Leistner

The fact that any representation of a compact Liegroup admits a positive definite invariant scalarproduct implies that there is an abundance of ir-reducible subgroups of O(n). For indefinite scalarproducts the situation is quite different. For ex-ample, for any n, the Lorentz group O(1,n) hasno irreducible subgroups apart from its connectedcomponent. We will show how this and a simi-lar classification result for irreducible, connectedsubgroups of O(2,n) follows from the Karpelevich-Mostov theorem. As an application we obtaina classification of irreducible conformal holonomygroups of conformal Lorentzian manifolds (This isbased on joint work with Antonio J. Di Scala, Po-litecnico di Torino, and with Jesse Alt, Universityof the Witwatersrand)

14.7. Subriemannian curvatures

Tohru Morimoto (Kinki University)


Tohru Morimoto

For each subriemannian manifold of constant sub-riemannian symbol we construct a Cartan con-nection canonically associated with this structure,which thereby enables us to define the curvaturesof the subriemannian manifold.

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14.8. On some generic distributions and theirautomorphism groups

Katharina Neusser (Australian National University)


Katharina Neusser

There is an interesting class of vector distribu-tions, which can be equivalently described as cer-tain types of parabolic geometries. Having intro-duced these types of distributions, we will showhow one can deduce just from the existence oftheir equivalence to certain parabolic geometriesstrong restrictions on the possible dimensions oftheir automorphism groups. This talk is based ona joint work with Andreas Cap.

14.9. Local obstructions to 2-dimensionalprojective structures admitting skew-symmetricRicci tensor

Matthew Randall (Australian National University)

16:00 Mon 26 September 2011 – 24.203

Matthew Randall

A projective surface is a 2-dimensional manifoldequipped with a projective structure i.e. a class oftorsion-free affine connections that have the samegeodesics as unparameterised curves. Given anyprojective surface we can ask whether it admitsa torsion-free affine connection (in its projectiveclass) that has skew-symmetric Ricci tensor. Thisis equivalent to solving a particular semi-linearoverdetermined partial differential equation. Itturns out that there are local obstructions to solv-ing the PDE in two dimensions. These obstruc-tions are constructed out of local invariants of theprojective structure.

14.10. (2, 3, 5)-distributions and associatedconformal structures

Katja Sagerschnig (Australian National University)


Katja Sagerschnig

A (2, 3, 5)-distribution is a maximally non-integrablerank 2 subbundle in the tangent bundle of a5-dimensional manifold. Based on fundamen-tal work of Elie Cartan, Pawel Nurowski showedhow to construct a conformal class of pseudo-Riemannian metrics of signature (2, 3) that isnaturally associated with such a distribution.This talk will be concerned with the applicationof parabolic geometry methods to the study ofNurowski’s conformal structures. I will discussjoint work with Andreas Cap and with MatthiasHammerl.

14.11. Howe duality for the symplectic Diracoperator

Petr Somberg (Charles University)


Petr Somberg

We find the Fisher decomposition for the space ofpolynomials valued in Segal-Shale-Weil represen-tation. As a consequence, this allows to determinesymplectic monogenics, i.e. the space of polyno-mial solutions of symplectic Dirac(-Kostant) op-erator.

14.12. Dunkl operators and a family of realizationsof osp(1|2)

Vladimir Soucek (Charles University)


Vladimir Soucek

A family of radial deformations of the realiza-tion of the Lie superalgebra osp(1|2) in the the-ory of Dunkl operators is obtained. This leadsto a Dirac operator depending on 3 parameters.Several function theoretical aspects of this oper-ator are studied, such as the associated measure,the related Laguerre polynomials and the relatedFourier transform. For special values of the pa-rameters, it is possible to construct the kernel ofthe Fourier transform explicitly, as well as the re-lated intertwining operator.

14.13. Twistor geometry in six dimensions

Arman Taghavi-Chabert (Masaryk University)


Arman Taghavi-Chabert

We describe twistor geometry in six dimensions,including the Penrose transform for zero-rest-massfields, in the language of spinors.

14.14. Geometric approach to partial differentialequations

Naghmana Tehseen (La Trobe University)


Naghmana Tehseen

The geometric study of differential equations aimsto describe the local and global structure of thesolutions as integral submanifolds of an equationmanifold. The study of partial differential equa-tions (PDEs) leads to the concept of Vessiot dis-tributions, which provides the convenient formalframework to investigate PDEs on an appropriatejet bundle. In this talk I will give a brief exposi-tion of Vessiot distributions of PDEs and then goon to describe some recent work.

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14.15. Rigidity of Schubert varieties in compactHermitian symmetric spaces

Dennis The (Australian National University)


Dennis The

Compact Hermitian symmetric spaces (CHSS) area distinguished class of homogeneous varietiesthat play a central role in algebraic and differentialgeometry. Their topology is well understood: inparticular, the homology of any CHSS G/P ad-mits a nice basis in terms of Schubert varieties.Most Schubert varieties are singular, and a nat-ural question is that of smoothability: Given aSchubert variety X[w] in a CHSS, does its homol-ogy class admit a smooth representative? Moregenerally, “how many” different representativesexist? If the only representatives are G-translatesof X[w], then X[w] is said to be Schur rigid. Us-ing a differential geometric approach, substantialprogress on the rigidity problem was made byMaria Walters, Robert Bryant, and Jaehyun Hongin the cases that X[w] is smooth or the CHSS isa Grassmannian. I will discuss work with ColleenRobles (Texas A&M) to study the rigidity of Schu-bert varieties in arbitrary CHSS using tools fromexterior differential systems, Lie algebra cohomol-ogy, and representation theory.

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15. Education Afternoon

15.1. Wallpaper, Crystals and Symmetry.

Michael Giudici (University of Western Australia)


Michael Giudici

Next time you are struggling to choose wallpaperand are faced with what seems like a myriad ofdifferent patterns, you will be relieved to knowthat a little mathematics proves that there are es-sentially only 17 patterns to choose from. I willdiscuss how group theory (the mathematical ab-straction of symmetry) can be used to make thisassertion. The same ideas are also used in crys-tallography to analyse the different possible struc-tures of crystals.

15.2. Fractals and Dynamics in Education

Michael Barnsley (Flinders University)

10:30 Thursday 29 September 2011 – Hope Theatre

RS Booth / ZA Melzak

I will present some accessible ideas, new to meand of pedagogical value, concerning fractal ge-ometry and dynamical systems. I will include ademonstration of the Fractal Camera.

93

Index of Speakers

Angeltveit, Vigleik (0.4), 52

Angeltveit, Vigleik (7.1), 73Angstmann, Christopher (4.1), 63

Aragon Artacho, Francisco Javier (6.1), 70

Atkinson, James (4.2), 63

Bandara, Menaka Lashitha (2.1), 58

Banerjee, Debargha (1.1), 54Barnsley, Michael (15.2), 93

Barnsley, Michael Fielding (14.1), 90

Bartlett, Nicholas (12.1), 85Beaton, Nicholas (13.1), 87

Bedini, Andrea (13.2), 87

Birrell, Andrew (13.3), 87Boland, Natashia (6.2), 70

Booth, Raymond (12.2), 85Borwein, Jonathan (3.1), 61

Brent, Richard P (10.1), 81

Brownlowe, Nathan (5.1), 68Bryan, Paul (2.2), 58

Bunder, Martin (1.2), 54

Butler, Samuel (4.3), 63

Cap, Andreas (14.2), 90

Challis, Vivien (3.2), 61Chiarella, Carl (9.1), 79

Cirstea, Florica (2.3), 58

Clutterbuck, Julie (2.4), 58Cowling, Michael (8.1), 77

Cox, Barry (4.4), 63

Crisp, Andrew (1.3), 54

Dancer, Edward Norman (2.5), 58

Daners, Daniel (2.6), 58De Gier, Jan (13.4), 87De Silva, Frank (13.5), 87

Deaconu, Valentin (5.2), 68Denier, Jim (4.5), 63

Devillers, Alice (10.2), 81

Do, Norman (7.2), 73Doust, Ian (12.3), 85

Du, Jie (1.4), 54

Du, Yihong (2.7), 58Duong, Xuan (8.2), 77

East, James (1.5), 54Eastwood, Michael (7.3), 73

Eberhard, Andrew Craig (6.3), 70

Egri-Nagy, Attila (1.6), 54Ehrgott, Matthias (6.4), 70

Elder, Murray (1.7), 55

Elfard, Ali Sayed (7.4), 73Ellinas, Demosthenes (13.6), 87

Engineer, Faramroze (6.5), 71

Fewster-Young, Nicholas (2.8), 59Fielding, Mark James (11.1), 83

Filar, Jerzy (6.6), 71Finn, Caley (13.7), 88

Forrester, Peter (13.8), 88

Francis, Andrew (4.6), 64

Gaitsgory, Vladimir (12.4), 85

Ganter, Nora (1.8), 55

Ganter, Nora (7.5), 73

Garoni, Timothy (13.9), 88Gebhardt, Volker (7.6), 73

Ghitza, Alex (1.9), 55Gillespie, Neil (10.3), 81

Giudici, Michael (1.10), 55

Giudici, Michael (15.1), 93Goard, Joanna (9.2), 79

Goldys, Ben (4.7), 64

Gover, Rod (14.3), 90Grotowski, Joseph (2.9), 59

Guo, Ivan (9.3), 79

Hall, Joanne (1.11), 55

Hamza, Kais (9.4), 79

Hanysz, Alexander (7.7), 74Hartley, David (2.10), 59

Hawkins, Stuart (3.3), 61

Henderson, Anthony (1.12), 55Henry, Bruce (4.8), 64

Hinic-Galic, Ana (14.4), 90

Ho, Bao (10.4), 81Hogan, Jeffrey (8.3), 77

Horadam, Daniel (1.13), 56

Howes, Philip (4.9), 64

Jhanjee, Sangeeta (1.14), 56

Jin, Qinian (3.4), 61Joshi, Nalini (0.1), 52

Joshi, Nalini (4.10), 64

Kang, Sooran (5.3), 68

Kim, Peter (4.11), 64

Koonin, Justin (1.15), 56Kumjian, Alexander (5.4), 68

Lamichhane, Bishnu (3.5), 62Langford, Mathew (14.5), 90

Larusson, Finnur (7.8), 74

Le Gia, Quoc Thong (3.6), 62Lee, Alex (13.10), 88

Leistner, Thomas (14.6), 90Leopardi, Paul (3.7), 62Li, Hui (5.5), 68Lian, Guanghua (9.5), 79

Liu, Shuangzhe (11.2), 83

Maenhaut, Barbara (10.5), 82

Mahanta, Snigdhayan (5.6), 68Mahanta, Snigdhayan (7.9), 74

Malkin, Peter (6.7), 71Maloney, Ben (5.7), 68Manyem, Prabhu (12.5), 85

Marangell, Robert (4.12), 64

Marquette, Ian (13.11), 88Matano, Hiroshi (0.7), 53

Mattei, Eduardo Cerutti (13.12), 89Mayhew, Dillon (10.6), 82

Mays, Anthony (13.13), 89

McCallum, Rupert Gordon (12.6), 86McCormick, Stephen Michael (2.11), 59

McCoy, James (2.12), 59

94

Index of Speakers

McCrae, Michaael (11.3), 83

McIntosh, Alan (2.13), 59

Mei, Lin-Feng (2.14), 60Memoli, Facundo (7.10), 74

Menon, Govind (4.13), 65

Merila, Ville (1.16), 56Miller, Boris (6.8), 71

Moghaddam, Amir (13.14), 89

Moitsheki, Joel (4.14), 65Morimoto, Tohru (14.7), 90

Morris, Andrew (8.4), 77Mungkasi, Sudi (3.8), 62

Neusser, Katharina (14.8), 91

Norton, Andrew (13.15), 89

Olenko, Andriy (11.4), 83

Oliynyk, Todd (2.15), 60Ong, Wilson (1.17), 56

Ormerod, John (11.5), 83

Ortiz, Omar (1.18), 56

Parkinson, James (1.19), 56

Paunescu, Laurentiu (7.11), 74Pettet, Graeme (4.15), 65

Pham, Hung Le (8.5), 77

Potgieter, Petrus H (3.9), 62Praeger, Cheryl (10.7), 82

Price, Christopher John (6.9), 72

Randall, Matthew (14.9), 91

Rennie, Adam (5.8), 69

Ritter, Tyson (7.12), 74Roberts, Mick (0.5), 52

Roberts, Mick (0.8), 53

Roberts, Tony (4.16), 65Rochon, Frederic (2.16), 60

Rodrigo, Marianito (9.6), 79

Sa Ngiamsunthorn, Parinya (2.17), 60

Sader, John (0.3), 52

Sagerschnig, Katja (14.10), 91Sanchez, Stephen James (12.7), 86

Santra, Sanjiban (2.18), 60

Seberry, Jennifer (10.8), 82Segerman, Henry (7.13), 75Seress, Akos (10.9), 82

Shymanska, Alla (4.17), 65Sims, Aidan (5.9), 69

Sims, Brailey (6.10), 72Sisson, Scott (11.6), 83

Somberg, Petr (14.11), 91

Soucek, Vladimir (14.12), 91Stanhope, Elizabeth (7.14), 75

Stuart, Robyn (4.18), 66Supasiti, Tharatorn (7.15), 75

Taghavi-Chabert, Arman (14.13), 91

Talebian, Masoud (6.11), 72Tehseen, Naghmana (14.14), 91

Thamwattana, Ngamta (4.19), 66

The, Dennis (14.15), 92Thomas, Anne (7.16), 75

Tod, Kenneth Paul (0.2), 52

Tran, Thi Dinh (4.20), 66Tran-Duc, Thien (4.21), 66

Triadis, Dimetre (4.22), 66

Tsarenko, Maria (13.16), 89

Wan, James (1.20), 57

Wang, Bryan (7.17), 75Wang, Xu-Jia (2.19), 60

Wang, You-Gan (11.7), 84

Webster, Samuel (5.10), 69Wechselberger, Martin (4.23), 67

Westerland, Craig (7.18), 75

Whittaker, Michael (5.11), 69Willis, George (0.6), 52

Willis, George (8.6), 77

Zhang, Tonghua (4.24), 67

Zhu, Song-Ping (9.7), 80

Zudilin, Wadim (1.21), 57

95

Index of Speakers

55

A

55

C55A

55C

55A

55C

NORTHFIELDS AVE

HA

RBO

UR

ST

SMITH ST

CO

RR

IMA

L ST

BURELLI ST

CROWN ST

PR

INC

ES H

WY

ELLIOTTS RDN

EW D

APT

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DM

ERCU

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T

FOLE

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GIPPS ST

CR

AW

FO

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PORTER ST

NORTHERN DIS

TRIBUTOR

SOU

TH

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FW

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SQU

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WA

Y

GEORGE HANLEY DR

KEM

BLA

ST

BOURKE ST

CLIFF R

D

YW

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NIR

P

RA

ILW

AY

CR

LEGEND

Bus 55C

Bus Stop

Bus Connection

Train ConnectionBus 55AAnti-clockwise

Clockwise

Walking Route

WOLLONGONG

NORTHWOLLONGONG

FAIRYMEADOW

WOLLONGONG

NORTHWOLLONGONG

FAIRYMEADOW

Buses9, 10, 11, 53, University Shuttle

University of Wollongong

University ofWollongongInnovationCampus

Wollongong HighSchool and Keira High School

WollongongHarbour

EntertainmentCentre

WollongongCity Beach

Corrimal St,Smith St

Greenacre Rd,Bligh St

Foley St

WollongongShopping District

WIN Stadium

Bourke St

Buses1, 3, 4, 6, 7, 8

Princes Hwy, Fairy Meadow

Buses1, 2, 3, 4, 6, 7, 8, 10, 11, 24, 32, 33, 34, 36, 37, 51, 53, 57, 65

Burelli St

Buses3, 6, 7, 8, 10, 11, 24, 32, 33, 34, 36, 37, 53, 57, 65

Keira St, Crown St

TrainsSouth Coast LineBuses9,10Loop operates weekend only

North Wollongong Station

TrainsSouth Coast Line

Wollongong Station

Buses24, 33, 34, 35, 36, 37, 39, 57

Wollongong Hospital

TAFE

Princes HwyElliotts Rd

Cnr Elliots Rd & Squires Way

Gipps St,Georges Pl

Mercury St

Only connecting services are shown at each stop

For further information on the Gong Shuttle call: Transport Info on 131 500 or visit 131500.com.au

SERVICE OPERATESMonday – Friday 7am-10pm7am-6pm every 10 minutes6pm-10pm every 20 minutesWeekends 8am-6pm every 20 minutes

96

KEY

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Contentsweb/@inf/@math/... · Contents Foreword 2 ... Special Sessions 1. Algebra and Number Theory...

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Transcript of Contentsweb/@inf/@math/... · Contents Foreword 2 ... Special Sessions 1. Algebra and Number Theory...