Canadian Undergraduate MathematicsConference 2016

University of Victoria

July 13th-17th, 2016

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Contents

1 Administrative Matters 31.1 Welcome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 WiFi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Food and Drink . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.4 Special Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.5 Transportation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.6 CUMC 2017 CCEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Schedules 72.1 Conference Schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Student Talk Schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3 Keynote Speakers 113.1 Keynote Bios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.2 Keynote Abstracts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4 Student Abstracts 15

5 Sponsors 40

6 Contacts 416.1 Conference Contacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416.2 Emergency Contacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

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1 Administrative Matters

1.1 Welcome

Welcome to CUMC 2016 at the University of Victoria! We are thrilled to be hosting you all. Please do not hesitate toask any of the volunteers in the navy shirts for assistance at any time.

Bienvenue au CCEM 2016 a l’universite de Victoria! On est excite de vous recevoir. S’il vous plait, n’importe quand,n’hesitez pas a demander de l’aide aux volontaires avec des chandails bleu fonce.

1.2 WiFi

To use internet while at CUMC, you may connect to eduroam with your regular university e-mail and password if youruniversity participates, or use CUMC WiFi. CUMC WiFi will be accessible in Residence, as well as CLE, COR, DSB,and the SUB (all the buildings in which we will operate).

Pour acceder a l’internet durant CCEM, vous pouvez choisir le resau eduroam, si votre universite participe. Ou, vouspouvez choisir le resau CUMC. Vous pouvez acceder au resau CUMC dans les residences, CLE, COR, DSB, et le SUB.

1.3 Food and Drink

On Campus

• Mystic Market: Open 8am-7pm, selections include sushi, salads, coffee, baked goods, and a bulk section.

• BiblioCafe: Open 8am-3pm Mon-Fri, selections include coffee, baked goods, salads and sandwiches.

• Student Union Building: On one end, there is the Munchie Bar, which serves (the best) coffee, baked goodsand sandwiches, open 8am-9pm Mon-Fri and 6pm-9pm Sat-Sun. On the other end, there is the International Grillserving burgers, salads and curry from 9am-3pm, Mon-Fr

Cadboro Bay

Cadboro Bay is a ten minute walk from the residences down Sinclair Rd. There is also a great beach and park at thebottom of Sinclair.

• Starbucks: Open 6:30am-9pm, selections include coffee and baked goods.

• Pepper’s Grocery: Open 8am-9pm, Mon-Fri and 8am-7:30pm, Sat-Sun, mid-sized grocery store including deli.

• Thai Lemongrass: Open 11am-2:30pm and 4:30pm-9pm, Thai food including vegetarian options.

• Mutsuki-An: Open 11:30-2pm and 4:30pm-8pm, Tues-Sat, Japanese food including sushi.

Tuscany Village

Tuscany Villagae is about a 30 minute walk from the residences, or five minutes from the bus depot by the number 16,26, or 39 bus.

• Thrifty Foods Open 24/7, full-sized grocery store.

• Mucho Burrito Open 10:30am-10pm Mon-Sat, and 10am-9pm Sun. Fast-food Mexican fare.

• Subway Open 7am-10pm Mon-Fri, and 9am-10pm Sat-Sun, serves submarine sandwiches.

• Original Joe’s Open 11am-Midnight, full bar and pub fare.

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Shelbourne Plaza

Shelbourne Plaza is about a 30 minute walk from the residences, or five minutes from the bus depot by the number 15bus.

• Fujiya Open 10am-7pm Mon-Fri, and 11am-6pm Sun. Serves great sushi-to-go, or made to order.

• Noodlebox Open 11am-9pm, a local Victoria chain who serves curries and stir-fries. Vegetarian and gluten-freeoptions available.

• Maude Hunter’s Open 11:30am-Midnight, full bar and pub fare.

• Pho-Ever Open 11am-9pm, serves Vietnamese food with vegan options.

1.4 Special Events

Opening Events

On Wednesday evening, we will be having our opening BBQ at 6:00 PM, after which participants may choose betweenwalking to a beautiful nearby beach for sports, games, or relaxation, and joining us at our campus pub, Felicita’s (19+).Meet outside the SUB at 7:30 to go to the beach, or 8:00 at Felicita’s in the SUB.

Evenements d’ouvertures

Le mercredi soir, on va avoir notre BBQ d’ouverture a 6 pm; apres, les participants peuvent choisir entre marcher a unebelle plage pour jeux, sports, et relaxation, ou venir nous joindre au pub du campus, Felicita’s (19+). Pour la plage, soyezen dehors du SUB a 7 :30 pm; pour Felicita’s, venez a 8 pm a Felicita’s dans le SUB.

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Mount Tolmie

On Thursday at 7:30 we will meet at DSB and walk to nearby Mount Tolmie for a short but rewarding hike. At the topyou will get a gorgeous view of the city of Victoria

Mont Tolmie

Jeudi a 19:30 nous allons nous rencontrer a DSB pour marcher jusqu’au mont Tolmie pour faire une randonnee. Ausommet il y a une vue magnifique de la ville de Victoria.

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Math Movie Night

On Thursday evening at 9:15, our campus theatre Cinecenta in the SUB is showing the Man Who Knew Infinity. Theyhave been kind enough to give all CUMC participants a discount- $4.75!

Soiree Cinema

Jeudi a 21:15, notre cinema sur le campus Cinecenta joue The Man Who Knew Infinity. Ils vont donner un billet a tarifreduit aux participants de CCEM- $4.75!

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Gender Diversity in Math Evening

On Friday, July 15th, we are hosting an evening dedicated to the celebration of Gender Diversity in Mathematics, anddiscussion surrounding the topic. The evening will consist of tapas and mingling, followed by a panel discussion, andfinishing with a dessert reception. Please note that you may only attend if you chose that option when registering.

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Soiree Diversite des genres en math

Le vendredi 15 juillet, nous aurons une soiree dediee a la celebration de la diversite des genres dans le domaine desmathematiques. Il y aura une discussion sur le sujet. La soiree consistera de tapas et de reseautage suivis d’un debat, letout couronne d’une reception dessert. Veuillez noter qu’il est possible de participer a la soiree seulement si vous l’avezchoisi durant votre enregistrement.

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Royal British Columbia Museum

The permanent displays at the Royal BC Museum take visitors from prehistoric British Columbia through to BC in the20th century, focusing on BC’s Natural History and First Nations.

Featured Exhibitions:

• Our Living Languages – “This interactive exhibition celebrates the resilience and diversity of First Nations languagesin BC in the face of change.”

• Mammoths: Giants of the Ice Age – “This engaging and interactive look at these magnificent creatures will transportvisitors to a time when giants walked among us and humans struggled to survive in a world they had yet to conquer.”

Musee Royal de la C.B.

La collection permanente du musee Royal BC amene les visiteurs de l’epoque de la prehistoire en colombie britanniquejusqu’au 20eme siecle take visitors from prehistoric British Columbia through to BC in the 20th century, focusing on BC’sNatural History and First Nations. Les expositions thematiques:

• Nos langues vivantes– “Cette exposition interactive celebre la resilience et la diversite des langues des premieresnations en Colombie-Britannique face a l’adversite.”

• Les mammouths: Les geants de l’ere glaciaire – “Ce regard engageant et interactif sur ces creatures magnifiquestransportera les visiteurs a une epoque ou les geants se promenaient parmi nous, et ou les humains luttaient poursurvivre dans un monde qui restait a conquerir”.

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Buskers’ Festival/Explore Downtown

The Buskers’ Festival features professional street performers from all over the world performing on stages throughoutDowntown Victoria. Entertainers in the festival include flame throwers, acrobats, magicians, jugglers, unicyclists, hulahoopers, giant puppets, balloonists, musicians and more! Watching the Buskers Festival is free, however it is a good ideato bring a few toonies or $5 bills to give to any buskers you find particularly entertaining!

Aside from the Buskers Festival, Downtown Victoria has some excellent attractions including:

• The scenic inner harbor (featuring the Parliament Building and the Empress Hotel)

• Beacon Hill Park

• Excellent shopping, food, and coffee

*Please note that you may only attend if you chose that option when registering.

Buskers’ Festival/Exploration de Centre-Ville

Le Buskers’ Festival represente des artistes de rue professionnels qui viennent de partout dans le monde; on les retrouve unpeu partout au centre-ville de Victoria. On trouve de tout: des cracheurs de feu, des acrobats, des magiciens, des jongleurs,des cyclists a une roue, des hula hoopers, des poupees geantes, des musiciens, des specialistes du ballon, et encore plusencore! Regarder le Buskers Festival est une activite gratuite, cependant il est toujours bon de donner quelques dollars al’artiste que vous aimez particulierement!

Le centre-ville de Victoria offre d’autres aspects/activites interessantes, tels que:

• Le port, incluant le batiment du parlement et l’hotel Empress Hotel

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• Le parc Beacon Hill

• D’excellents magasins, restaurants et cafes

* Veuillez noter qu’il est possible de participer a la visite au centre-ville seulement si vous l’avez choisi durant votreenregistrement.

1.5 Transportation

You can find bus maps and schedules at bctransit.com/victoria/. Bus numbers 14, 15, and 4 all run between UVic anddowntown.

Vous pouvez trouver des plans et horaires d’autobus a bctransit.com/victoria/. Les autobus 4, 14, et 15 circulententre l’universite et le centre-ville.

1.6 CUMC 2017 CCEM

If you’re having fun at this year’s CUMC, consider bringing it back home with you for the rest of your department toenjoy. Submit a bid to host next year’s CUMC 2017! The bidding process for next year’s CUMC is detailed at the Studcwebsite at studc.math.ca/?page_id=107. The bid is due two weeks after the last day of the CUMC, July 31st.

Amusez-vous bien au CCEM? Profitez de l’occasion de soumettre une candidature pour le CCEM de l’annee prochaine etrapportez le CCEM a votre departement! Le processus de mise en candidature pour le CCEM prochaine est explique endetail au site web de Studc a studc.math.ca/?page_id=107. Le formulaire est a echeance deux semaines apres le dernierjour du CCEM, le 30 juillet.

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2 Schedules

2.1 Conference Schedule

Wednesday, July 13th / Mercredi, le 13 juillet

12:30-3:30pm SUB - Upper Lounge Registration / Enregistrement

4:00-4:30pm DSB C103 Opening remarks / Discours d’ouverture

4:30-5:30pm DSB C103 Keynote speaker / Conferencier principal: Mary Lesperance

6:00-7:30pm Village Greens Opening BBQ / BBQ d’ouverture

7:30pm Meet outside SUB Beach Walk / Promenade a la plage

8:00pm Felicita’s Campus Pub Opening reception / Reception d’ouverture (19+)

Thursday, July 14th / Jeudi, le 14 juillet

8:30-11:00am COR A225, A229, B143 Student talks / Conferences etudiantes

11:00-11:20am DSB C126 Coffee break / Pause de cafe

11:20-12:20pm DSB C103 Keynote speaker / Conferencier principal: Boualem Khouider

12:30-2:00pm SUB - Vertigo Lunch and roundtable discussions / Lunch et discussions informelles *

2:00-4:00pm CLE A203, A207, A211 Student talks / Conferences etudiantes

4:20-5:20pm DSB C103 Keynote speaker / Conferencier principal: Kseniya Garaschuk

7:30pm Meet outisde DSB Optional hike up Mount Tolmie / Randonne au Mont Tolmie, optionelle

9:15pm SUB - Cinecenta Optional movie / Film optionelle: The Man Who Knew Infinity

Friday, July 15th / Vendredi, le 15 juillet

8:30-11:00am COR A225, A229, B143 Student talks / Conferences etudiantes

11:00-11:20am DSB C126 Coffee break / Pause de cafe

11:20-12:20pm DSB C103 Keynote speaker / Conferencier principal: Greg Martin

12:30-2:00pm SUB - Vertigo Lunch and roundtable discussions / Lunch et discussions informelles

2:00-4:30pm CLE A203, A207, A211 Student talks / Conferences etudiantes

4:40-5:40pm DSB C103 Keynote speaker / Conferencier principal: Kristine Bauer

7:00-10:00pm BWC Gender diversity event / Soiree pour la diversite de genre:

7:00-8:00pm BWC 101 Tapas

8:00-9:30pm BWC A104 Panel discussion / Table ronde avec invites

9:30-10:00pm BWC 101 Dessert

Saturday, July 16th / Samedi, le 16 juillet

8:30-11:00am COR A225, A229, B143 Student talks / Conferences etudiantes

11:00-11:20am DSB C126 Coffee break / Pause de cafe

11:20-12:20pm DSB C103 Keynote speaker / Conferencier principal: Audrey Yap

12:30-1:20pm SUB - Vertigo Lunch

1:30-5:00pm DSB Trip downtown / Voyage au centre-ville: Busker’s Festival & Museum

6:30-9:00pm University Club Closing banquet / Banquet de fermeture

Sunday, July 17th / Dimanche, le 17 juillet

9:00-10:30am COR A225, A229, B143 Student talks / Conferences etudiantes

10:30-12:00pm SUB - Vertigo Brunch

12:30-1:30pm DSB C103 Keynote speaker / Conferencier principal: Peter Dukes

1:30-2:30pm DSB C103 Closing remarks / Remarques de fermeture

∗ Sponsored by the Graduate Program with the Department of Mathematics & Statistics!

Commanditee par le programme d’etudes graduees du departement de mathematiques et statistiques!

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2.2 Student Talk Schedule

Thursday, July 14th/ Jeudi, le 14 juillet

COR A225 COR A229 COR B143

8:30amJohn Sardo - Linear

Programming: Theory andApplications

Bryan Coutts - Intro toQuantum Computing

Laura Gutierrez Funderburk -On the Chromatic Number of

Latin Square Graphs

9:00amAdam Humeniuk - SimplicialHomology and its Algorithmic

Computation

Aiden Huffman - Analysis andReconstruction of a Trace Norm

Inequality

Seth Friesen - Recursive GraphExpansions of Feynman

Diagrams

9:30amStefan Dawydiak -

Representation Theory ofSL(2,R)

David Pechersky - TheBeurling-Gelfand Spectral

Radius Formula

Shayla Redlin - The FirefighterProblem for All Orientations of

the Hexagonal Grid

10:00amBowen (Coco) Tian -

Representations and Charactersof Finite Groups

Adriano Pacifico - Continuingthe Story: A Story of Analytic

Continuation

Haggai Liu - The Cone ofWeighted Graphs Generated by

Triangles

10:30amAyoub El Hanchi - Quaternionic

Exponentials and PossibleApplications

Adam Artymowicz - A Proof ofWeyl’s Equidistribution

Theorem

Kel Chan - The CombinatorialAspect of Surface Classification

Theorem

CLE A203 CLE A207 CLE A211

2:00pmAaron Slobodin - Syzygies and

Betti Tables: A Taste ofComputational Algebra

Daniel Hudson - A Pathology inAnalysis

Guo Xian Yau - QuantumGames: When Classical Games

Just Aren’t Enough

2:30pmDaniel Satanove - Propositions

as Types as SpacesMengxue Yang - Things I

Learned About Gauss-BonnetSwapnil Daxini - An

Introduction to RSA Encryption

3:00pmCalder Morton-Ferguson - Why

Some Sequences are MoreSpecial than Others

Dylan Cant - Geometric Flowson Warped-Product Surfaces

Zishen Qu - TheNo-three-in-line Problem

3:30pmAlexandre Zotine - The Class

Group and Ideal NumbersYuan Yao - Riemannian

Geometry

Reginald Lybbert -Exponentiation Methods for

Ideals in Real Quadratic Fields

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Friday, July 15th/ Vendredi, le 15 juillet

COR A225 COR A229 COR B143

8:30amLena Ruiz - The Mathematics of

Music

Kyle MacQuin - PartialDifferential Equations and

Population Dynamics

Shouzhen Gu - QuantumCryptography and the Key Rate

Problem

9:00amFoster Tom - Schur-Positivity of

Equitable Ribbons

Chelsea Uggenti - Investigatingthe Stability of Disease Models

with Temporary Immunity

Maxwell Allman - Complexity ofLinearly Parametrized Min Cut

Networks

9:30amTrevor Vanderwoerd - BoundingPolynomial Roots Using Matrix

Norms

Chadi Saad-Roy - A Model ofBovine Babesiosis Including

Juvenile Cattle

Xinrui Jia - Public KeyExchange Using Semidirect

Products

10:00amDuncan Ramage - How to Add

Infinity to Infinity: TheArithmetic of Cardinal Numbers

Sean La - Phylogenetic TreeConstruction Using

Computational Methods

Kevin Zhou - Markov Chainsand n-dimensional Lattice

Random Walks

10:30am

Kyle MacDonald - Talk AboutMath and Take Our Money: AnUpdate from the CMS Student

Committee

Amir Farrag - Exactly SolvablePotentials and Orthogonal

Polynomials

Liam Wrubleski - OptimalCourse Scheduling

CLE A203 CLE A207 CLE A211

2:00pmGuthrie Prentice - Does

Mathematics Exist?Clair Dai - Representation

Theory and Particle PhysicsSam Jaques - Intersecting Sets

in Two-Transitive Groups

2:30pm

Nam-Hwui Kim - A ReallyGentle Introduction to EM:

What it is and Why it’sAwesome

Roy Magen - The InterchangeLaw and the Eckmann-Hilton

Argument

Brandon Elford - AnIntroduction to Ramsey Theory

on Graphs

3:00pmYan Zhang - Life Insurance:

From Zootopia to Reality

Shelley Wu - TheRobinson-Schensted-Knuth

Correspondence

Mariia Sobchuk - ClassifyingLeafsets and Determining

Existence of Opposite Trees

3:30pm

Robert Zimmerman - FiniteMixtures of Nonparametric

Regression Models withGeneralized Additive

Components

Henry Liu - The Number ofDegree d Curves Passing

through 3d− 1 Points in thePlane

Ilia Chtcherbakov - GraphHomomorphisms and Cores

4:00pmMatthew Jordan - Math and

Comedy: An Unlikely RomanceJason Lynch - An Introduction

to Continued Logarithms

Angela Wu - The ChromaticNumber of the Plane and the

Axiom of Choice

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Saturday, July 16th/ Samedi, le 16 juillet

COR A225 COR A229 COR B143

8:30amReila Zheng - An Introduction

to Non-Standard CalculusLuke Polson - Simple is Elegant

Matthew Sunohara - Drawingsof Complete Graphs

9:00am

Laura Chandler - Mathematicaland Computational Modeling of

Spring-time Convection inLakes

Gregorio Arturo Reyes Gonzales- Geodesics

Ethan White - BoundingSymmetry in Colour

9:30amJacob Denson - On Molecular

Gases and the Natural Numbers

Wes Chorney - The c2Invariants of Some Symmetric

Graphs

Tina Cho and David Charles -Capacitated Vehicle RoutingProblem in Python and/or R

10:00amTaras Kolomatski -

Stone-Weierstrass by FunctionalAnalysis

Zachary Karry - Sphere Packingand the Baffling Properties of

the E8 and Leech Lattices

Fatima Davelouis - AnIntroduction to the Single and

Double-ExponentialSinc-Collocation Method

10:30amMichael Oliwa - Orthogonality

and Angular Measures inNormed Spaces

Dillon Burgess - Bay of FundyTidal Power: Re-Analysis of

Tidal Velocity Data

Simon Huang - A BriefIntroduction to Bin Packing

Sunday, July 16th/ Dimanche, le 16 juillet

COR A225 COR A229 COR B143

9:00amJesus Miguel Martınez

Camarena - Rasiowa-Sikorski:Back and Forth Again

Kyle MacDonald - Heat Flowand Brownian Motion

Aashi Aman - Learn How toCalculate in Seconds!

9:30am

Matthew Pietrosanu -Uncovering Structure in Data

with Persistent Homology:Theory and Linguistic

Applications

Tyler Hofmeister - Algorithmicand High Frequency Trading:The Mathematics of the Limit

Order Book

Casie Bao - Compressed Sensingwith Corruptions

10:00amSohraub Pazuki - Socialist

Prime Numbers and aComposite Analogue

Koen van Greevenbroek -Planar Maps and the Largest

Face-degree

Sam Fisher - Symmetries of theRayleigh Wave Equation

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3 Keynote Speakers

3.1 Keynote Bios

Kristine Bauer

Kristine Bauer is an assistant professor in the Department of Mathematics and Statistics at the University of Calgary.

She received her Ph. D. in 2001 for her thesis ”Splittings of the Goodwillie Tower for Functors of Hopf Algebra Type”,

which was completed under the supervision of Dr. Randy McCarthy. During 2001 - 2003, she completed postdoctoral

work at Johns Hopkins University and the University of Western Ontario. Dr. Bauer’s research is in homotopy theory,

specifically in functor calculus. She is one of the founders of the Women in Topology network, and a leader of the WIT

functor calculus teams. In addition to her research, she also enjoys teaching and mentoring. She is a recipient of the

Faculty of Graduate Studies Great Supervisor award, and was recently nominated for the Faculty of Science Established

Career Teaching Excellence Award at the University of Calgary.

Peter Dukes

Peter Dukes is an associate professor in the Department of Mathematics and Statistics at the University of Victoria. He

studied mathematics as an undergraduate at UVic, then earned an M.Sc. from the University of Toronto and a Ph.D.

from Caltech. His research interests focus on combinatorics, although he enjoys beautiful mathematics in many areas.

Kseniya Garaschuk

Kseniya Garaschuck is a Science and Teaching Learning Fellow in the Department of Mathematics at the University of

British Columbia. She received her PhD in Mathematics from the University of Victoria in 2008. Her educational research

interests mainly concern exploring the effects of precalculus knowledge review on students’ performance in a calculus

course as well as developing effective ways of implementing such review. She is also interested in studying connections

between procedural and conceptual knowledge and how proficiency in one reflects in the other.

Boualem Khouider

Boualem Khouider is a professor in the Department of Mathematics and Statistics at the University of Victoria. He

received his PhD in 2002 from the University of Montreal. His research interests include climate modelling, numerical

analysis, fluid dynamics, stochastic models, and specifically the study of the interactions between planetary scale tropical

waves and cumulus convection.

Mary Lesperance

Dr. Mary Lesperance is a full professor of Statistics in the Department of Mathematics & Statistics. Dr. Lesperance

received her doctoral degree in Statistics from the University of Waterloo in 1990 at which time she joined McMaster

University, moving to the University of Victoria in 1992. She is founding director of the Statistical Consulting Centre, a

centre that offers statistical advice and services to researchers both at the university and beyond. This position has given

her an appreciation for a wide spectrum of research areas. Mary has served on grant selection committees and she has been

involved with the Statistical Society of Canada in several capacities. Mary is an active researcher and graduate student

supervisor who enjoys and seriously takes on her role as teacher and mentor. Her current projects include: creating models

to quickly differentiate true TIA (mini-strokes) symptoms from similar clinical presentations, analysis of tadpole genomic

data from toxicology experiments and theoretical mixture models used to model clustered data.

Greg Martin

Greg Martin is a professor in the Mathematics Department of the Unviersity of British Columbia in Vancouver. He grew

up in the US before moving to Canada in 1998 and Vancouver in 2001. His research interests lie primarily in classical

multiplicative number theory (very much related to the topic of his lecture) as well as the distribution of prime numbers.

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He is a two-time winner of the Mathematical Association of America’s Lester R. Ford Award for ”articles of expository

excellence published in the American Mathematical Monthly”. Outside of work, he swing dances regularly, sings in a

contemporary classical men’s choir, and plays ultimate frisbee when he gets the chance.

Audrey Yap

Audrey Yap is an Associate Professor in the Department of Philosophy at the University of Victoria. She completed her

undergraduate work at the University of British Columbia and her PhD at Stanford University. She currently teaches and

researches in logic and the philosophy of mathematics, as well as in feminist philosophy.

3.2 Keynote Abstracts

Kristine Bauer (University of Calgary)

The Chain Rules

The chain rule for differentiable functions of a real variable is one of the most familiar formulas involving differentiation.

Iterating the familiar formula leads to a formulation of a higher order chain rule which gives the n-th derivative of g

composed with f in terms of the derivatives of g and f. In 1855, Francesco Faa di Bruno gave a beautiful formulation of

this higher order chain rule. The coefficients of the terms in the formula can be counted using expressions in terms of trees,

partitions and other beautiful combinatorial constructions. These constructions might not seem immediately relevant to

differentiation, until you examine the formula more closely.

The Faa di Bruno construction is formulated for functions of a single variable, and does not lend itself well to the

directional derivative for functions of several variables. Unlike derivatives for functions of a single variable, iterating the

directional derivative requires one to keep track of the choices of direction that were made at each iteration. A 2005

paper of Huang, Marcantognini and Young describes a very nice formulation of the higher order chain rule for directional

derivatives.

In this talk I will explain the combinatorics of the Faa di Bruno formula as well as the higher order chain rule for

directional derivatives, and I’ll explain what these two formulas have to do with each other. I was originally drawn to

formulations of the chain rule because of applications of this formula in algebraic topology which I have explored in joint

work with B. Johnson, E. Riehl, C. Osborne and A. Tebbe. If time permits, I will explain that work.

Peter Dukes (University of Victoria)

A Survey of Permutation Codes

Classical coding theory is concerned with packing binary words subject to certain prescribed distance requirements.

In a little more detail, the set of binary words {0, 1}n is equipped with a metric known as Hamming distance dH , where

dH(u, v) counts the positions in which words u and v disagree. Given integers n and d, one is interested in ‘codes’

C ⊆ {0, 1}n such that dH(u, v) ≥ d for any distinct u, v ∈ C. Good codes can be used for data compression or transmission

over a noisy channel. Finding the largest such C is a discrete optimization problem roughly analogous to packing spheres.

This talk will investigate the coding theory of permutations, in the sense that we replace the cube {0, 1}n with the

symmetric group Sn, retaining dH as above to measure distances. With this in mind, let M(n, d) denote the maximum

size of a set Γ ⊆ Sn such that, for any distinct σ, τ ∈ Γ, at most n−d points are fixed by στ−1. For example, M(n, n) = n

and M(n, 1) = M(n, 2) = n!.

The investigation of permutation codes connects with various topics in combinatorics and algebra. This talk will

survey some of these connections and summarize what is known on M(n, d). There are plenty of open questions and even

applications to real-world problems in information theory.

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Kseniya Garaschuk (University of British Columbia)

On Teaching, Studenting, and Researching

As individuals, we each bring our own experiences, interests and backgrounds into our classrooms. As educators, we

do our best to present the material in the most clear and logical manner. But those two things need not be disjoint: the

content of a course is usually fixed, but the presentation of it need not be. After all, an average student’s affair with math

is too short for examples that seem to only emphasize the difference between math textbooks and real life (enough with

ladders sliding down walls already). It is my firm belief that students should see math as both a creative problem solving

discipline and as a personal, social and relevant to them activity.

As a math education researcher, I am also interested in studying the feasibility and effectiveness of implemented

techniques and activities from both the student and instructor perspectives. Determining what students should learn,

scientifically measuring what they are learning and adapting teaching methods to improve student learning are at the

heart of math education as a discipline.

In this talk, I will discuss how I inject inspiration from my out-of-classroom life into my teaching. I will present some

concrete examples and activities based on authentic applications that are relevant to students. I will then discuss how

to introduce and test new practices in your own teaching. In particular, we will talk about how to set up an experiment

to study a classroom activity. To illustrate the latter, I will use an example of my most recent study of feasibility and

effectiveness of collaborative/group exams in large mathematics courses.

Boualem Khouider (University of Victoria)

Mathematics of clouds: An outstanding challenge in climate change science

Research in pure mathematics and research in applied mathematics differ in large at the root, i.e, from the motivational

stand-point. While in pure mathematics research problems are mainly driven by pure curiousity and desire for deeper

understanding of given concepts and mathematical objects, research in applied math starts from a practical problem often

originating from a disctant discipline of science or engineering which the mathematician is ought to learn, sometimes on

the job! My talk on cloud modeling in climate science will start with a brief introduction of the atmospheric physics which

pertains to clouds.

Atmospheric convection is the process through which warm and moist air parcels rise from the surface, condense liquid

water and form cumulus clouds. This often results in heavy precipitation and massive storms; The process of condensation

is accompanied by the release of latent heat, which is associated with the phase change of water from vapor to liquid

and/or ice. In the tropics, moist convection constitutes a major source of energy for both local and large-scale circulations.

Precipitation patterns in the tropics are organized into cloud clusters and super-clusters involving a wide range of scales:

from the convective cell (the cumulus cloud) of 1 to 10 km, to planetary scale waves with oscillation periods of 40 to 60

days. Due to the complex interactions between the local processes of convection and the large scale waves, climate models

fail to properly capture tropical circulation patterns and their effect on the global circulation. In a climate model, the

governing equations are discretized on a coarse mesh of roughly 100 km to 200 km and the effects of processes that are

not resolved on such grids are represented by parameterizations also called sub-grid models. According to the last report

of the United Nations’ Intergovernmental Panel on Climate Change (IPCC), the interactions of clouds and the climate

system constitutes one of the major incertainties in the current climate models.

In this talk, I will survey some novel ideas on how to represent climate variability due to interactions with clouds and

convection processes in the state-of-the-art climate models, using stochastic particle interacting systems borrowed from

statistical mechanics. This leads to elegant Markov chain models for the area coverage of various cloud types, that are

easily integrated into the climate models.

Mary Lesperance (University of Victoria)

Assessing conformance with Benford’s Law: goodness-of-fit tests and simultaneous confidence inter-

vals

13

Benford’s Law is a probability distribution for the first significant digits of numbers, for example, the first significant

digits of the numbers 871 and 0.22 are 8 and 2 respectively. The law is particularly remarkable because many types of

data are considered to be consistent with Benford’s Law and scientists and investigators have applied it in diverse areas,

for example, diagnostic tests for mathematical models in Biology, Genomics, Neuroscience, image analysis and fraud

detection.

In this talk we present and compare statistically sound methods for assessing conformance of data with Benford’s

Law, including discrete versions of Cramer-von Mises (CvM) statistical tests and simultaneous confidence intervals. We

demonstrate that the common use of many binomial confidence intervals leads to rejection of Benford too often for truly

Benford data. Based on our investigation, we recommend that the CvM statistic U2d , Pearson’s chi-square statistic and

100(1−α)% Goodman’s simultaneous confidence intervals be computed when assessing conformance with Benford’s Law.

Visual inspection of the data with simultaneous confidence intervals is useful for understanding departures from Benford

and the influence of sample size.

Greg Martin (University of British Columbia)

Statistics of the Multiplicative Group

For every positive integer n, the quotient ring Z/nZ is the natural ring whose additive group is cyclic. The ”multi-

plicative group modulo n” is the group of invertible elements of this ring, with the multiplication operation. As it turns

out, many quantities of interest to number theorists can be interpreted as ”statistics” of these multiplicative groups. For

example, the cardinality of the multiplicative group modulo n is simply the Euler phi function of n; also, the number of

terms in the invariant factor composition of this group is closely related to the number of primes dividing n. Many of

these statistics have known distributions when the integer n is ”chosen at random” (the Euler phi function has a singular

cumulative distribution, while the Erdos-Kac theorem tells us that the number of prime divisors follows an asymptotically

normal distribution). Therefore this family of groups provides a convenient excuse for examining several famous number

theory results and open problems. We shall describe how we know, given the factorization of n, the exact structure of the

multiplicative group modulo n, and go on to outline the connections to these classical statistical problems in multiplicative

number theory.

Audrey Yap (University of Victoria)

Algebra and the Philosophy of Mathematics

Structuralism in the philosophy of mathematics encompasses a range of views, many of which see structures, such as the

entire system of natural numbers, as the proper objects of mathematics, rather than objects like individual natural numbers.

This talk will look at the way in which mathematical contributions by Emmy Noether, some extending Richard Dedekind’s

work, constitute a transition in mathematics that enables a fuller range of structuralist positions. Mathematics itself needed

to be conducive to a treatment of structures as objects in their own right before some contemporary philosophical positions

could make sense. Noether’s work in algebra and invariant theory is a perfect illustration of the kind of conceptual step

that permits seeing structures themselves as objects.

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4 Student Abstracts

Complexity of Linearly Parametrized Min Cut Networks

Maxwell Allman

Optimization (University of British Columbia )

A network is a directed graph where each edge is assigned a non-negative value, called a capacity. Given two vertices

in the network, s and t, an s-t cut is a partition of the graph into two parts, S and T, where s ∈ S and t ∈ T . The capacity

of an s-t cut is the sum of the capacities of the edges from vertices in S to vertices in T. The s-t cut that has the minimum

capacity is called the min-cut; the Max-Flow Min-Cut Theorem states that the capacity of the min-cut equals the max

flow from s to t. I will discuss the number of distinct min-cuts that can exist when the edge capacities are linear functions

of k parameters, as the parameters vary. Conditions will be given for which such networks either have their number of

distinct min-cuts bounded by a polynomial in |G|, or for which there exists a construction which gives an exponential

number of min-cuts. This problem relates to the algorithmic complexity of problems such as finding the max flow over all

param! eter values.

Talk prerequisites: None

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Learn How to Calculate in Seconds!

Aashi Aman

History of Math (University of Victoria)

If you have ever wondered how Scott Flansburg (Fastest Human Calculator) does his job, then this is the right talk

for you . I’m not talking about complicated formulas and derivations. Let’s go back to the basics, back to grade 3 when

all we knew about Math was addition, multiplication, subtraction and division. Back to the ancient time. Surprisingly ,

people like Scott Flansburg or Shakuntala Devi (known as ‘Human Calculators’) use ancient techniques to calculate huge

sums like multiplication of two four- digit numbers or deriving the square root of 5-digit number in seconds! Join me for a

quick 20 minute talk glimpse about about a brief introduction to ancient mathematics and the techniques evolved during

that time to make calculations simplier.

Talk Prerequisites: None

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A Proof of Weyl’s Equidistribution Theorem

Adam Artymowicz

Analysis (University of Toronto)

If you’re tired of zoning out halfway through a talk and spending the remainder staring into space, this one’s for

you. In this talk I’ll prove Weyl’s equidistribution theorem (who would have guessed?). The proof is neither long nor

technical. It is, in my opinion, a pretty neat little proof. The only background I require is basic real analysis (you should

be comfortable with delta-epsilon proofs), and I will present at a leisurely pace. Here’s a taste: Let x be a real number

between 0 and 1. Call the set of fractional parts of all integer multiples of x its ’orbit’. In other words, the orbit of x is

¡nx¿ : n a natural number, where ¡a¿ is the fractional part of a (ie. a - floor(a) ). It’s a relatively easy-to-prove fact that

if x is irrational, then the orbit of x is dense in [0,1]. In fact, more is true: the orbit of an irrational number is, in some

sense, evenly distributed on [0,1]. Talk difficulty: two chili peppers out of a possible five.

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Talk prerequisites: basic real analysis.

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Compressed Sensing with Corruptions

Casie Bao

Compressed Sensing (Simon Fraser University)

A major problem in signal and image processing is to recover a signal or image from undetermined sets of measurements.

Rather than the traditional sampling at a high rate and then compress the sampling data, compressed sensing (CS) allows

us to directly sense the data at a lower sampling rate. This research focuses on a natural generalization of compressed

sensing- CS with corruptions, which is to address the signal recovery problem when the measurements are corrupted

and become unreliable. The mathematical interpretation of this problem is as follows: minx,f ‖x‖1 + λ‖f‖1 subject to

Ax+ f = y. This talk will present that under different values of lambda, the largest fraction of corrupted measurements

one can tolerate in order to recover a signal with certain sparsity, and thus show the optimal lambda for the above

optimization problem. One of the practical applications of CS with corruptions is to deal with the scanning error occurred

in the clinical! MRI scan.

Talk prerequisites: Linear Algebra

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Bay of Fundy Tidal Power: Re-Analysis of Tidal Velocity Data

Dillon Burgess

Tidal Power (Acadia University )

Models have indicated that 2500 MW of energy could be extracted from the tidal currents of the Bay of Fundy.

Harnessing the energy of the Bay of Fundy has proved to be a difficult task, with the characteristics of the tidal currents

needing to be analyzed and understood before a turbine can enter the water. Using a cabled Acoustic Doppler Current

Profilers (ADCP), a year long data set of the tidal velocity at a location in Grand Passage was gathered. Unfortunately,

the data sets have several data gaps, when the instrument malfunctioned. The ADCP data can be analysed by performing

a harmonic analysis, which produces amplitudes and phases of the tidal constituents. Each tidal constituent represents

how an aspect of the periodic change in the relative positions of the Earth, Moon and Sun contributes to the time series

data. Tidal velocities can then be reconstructed with the results from the harmonic analysis to generate a continuous

time series for a full year.

Talk prerequisites: None

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Rasiowa-Sikorski: Back and Forth Again.

Jesus Miguel Martınez Camarena

Set Theory and Mathematical Logic (Universidad Nacional Autonoma de Mexico/ University of Regina)

In Set Theory, the technique of forcing is an amazing tool. It allow us to generate models for axioms, which are

”forced” to satisfy some special properties (e.g. C.H.), providing a way to proof their independence and consistency. A

fundamental part of this technique is the Rasiowa-Sikorski Lemma, that allows us to extend certain objects, devising

”new” ones that both enhance and carry with them some desirable properties. In spite of its simplicity, it encloses a clever

perspective to work with basic set theoretical concepts (such as orders and compatibilty) and combines to obtain amazing

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results. This Lemma is usually introduced via some heuristic applications in order to better understand its mechanisms.

Between others, this result holds important similarities with the constructive method of back and forth. I find this result

really beautiful, and will present both the lemma and some heuristic approaches, as well as a discussion of these concepts

in a simple and friendly way.

Talk prerequisites: Basic Set Theory

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Geometric Flows on Warped-Product Surfaces

Dylan Cant

Differential Geometry and Geometric Analysis (McGill University)

A warped-product surface is a two-dimensional Riemannian manifold with a particular choice of Riemannian metric. In

my talk, I will discuss evolving closed curves in warped-product surfaces according to certain partial differential equations.

I will begin my talk by carefully defining the prerequisite notions: topological spaces, manifolds, differentiable spaces,

differentiable manifolds, Riemannian manifolds, submanifolds and submanifold flows. Then we will apply these notions to

the problem of evolving closed curves on warped-product spaces, and I will present an existence and uniqueness theorem

concerning evolution of curves according to a particular geometric flow.

Talk prerequisites: Multivariable Calculus

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The Combinatorial Aspect of Surface Classification Theorem

Kel Chan

Graph Theory (Simon Fraser University)

The Surface Classification Theorem says that all compact 2-manifolds are essentially tori or projective planes. This is

an intuitive yet complex result first “proved” by Mobius and Jordan in 1866. Over next 41 years, the pursue of a rigorous

proof inspired significant development in modern mathematics. In this talk, we will retrace its steps with emphasis on

the combinatorics of cell complexes. The audience will be introduced to handles, crosscaps, and invariants of surfaces such

as orientation, fundamental group, and cell complex. We will also see several ways to visualize and construct orientable

and unorientable surfaces.

Talk prerequisites: Elementary topology

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Mathematical and Computational Modeling of Springtime Convection in Lakes

Laura Chandler

Fluid Mechanics (University of Waterloo)

Fluid mechanics is all around us- from the kilometers of atmosphere above our heads, to the intricate swirls of cream

in coffee, to the blood flowing through our veins. Each of these fluid flows can be mathematically modelled by a system

of nonlinear partial differential equations that describe the fluid’s conservation of mass, energy, and momentum. Due

to the complexity of these equations, most interesting cases must be solved numerically. These solutions can be used to

create beautiful simulations that tell us about the behaviour of a physical system. In particular, this talk will focus on

the application of these simulations to springtime convection in lakes which occurs near freshwater’s maximum density at

4 degrees Celsius. This is the driving mechanism that causes cooler lakes to overturn and become stratified as they are

heated by the sun. We will also discuss the importance of laboratory experiments to supplement mathematical ideas.

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Talk prerequisites: None

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Capacitated Vehicle Routing Problem in Python and/or R

Tina Cho & David Charles

Optimization (Carleton University)

Given a simple Constrained Vehicle Routing Problem, with 10 customers, 3 drivers and a single depot, we will attempt

to find a fast and efficient solution that will scale well in a parallel processing environment.

Talk prerequisites: R and Python languages

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The c2 Invariants of Some Symmetric Graphs

Wes Chorney

Graph Theory (Simon Fraser University)

The c2 invariant is a graph invariant introduced by Schnetz to better understand Feynman integrals. It has or is

conjectured to have the same symmetries as the Feynman period (a key piece of the Feynman integral).

To define the c2 invariant, we must first define the Kirchhoff polynomial. Given a graph G, ψG =∑T⊂G

∏e/∈T ae,

where the sum runs over all spanning trees of G and the ae are edge variables of G. Then the c2 invariant is

c(p)2 =

[ψG]pp2

(mod p)

where p is a prime and [ψG]p is the number of points in the affine algebraic variety of ψG over Fp, the finite field with p

elements. The affine variety is in many cases cumbersome to work with, and so alternative expressions for the c2 invariant

exist in terms of Dodgson and spanning forest polynomials.

This talk looks at computing the c2 invariant by exploiting the symmetry of graphs with appealing structure.

Talk Prerequisites: Basic Graph Theory

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Intro to Quantum Computing

Bryan Coutts

Analysis and Optimization (University of Waterloo)

Despite the intimidating name, quantum computation has a simple, physics-less mathematical model. Roughly, quan-

tum computations amount to applying unitary transformations and taking projections in a complex vector space. We will

precisely establish this model of quantum computation. We will then analyze the Deutsch-Jozsa problem, which classically

requires exponentially many queries to solve, but can be solved by a quantum algorithm with only a single query.

Talk prerequisites: Linear Algebra 1; no physics required

—————————————————————————————

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Graph Homomorphisms and Cores

Ilia Chtcherbakov

Algebraic Combinatorics (University of Waterloo)

A graph homomorphism is an edge-preserving map of the vertices. Many basic questions about graphs can be stated

in terms of the existence of homomorphisms between certain graphs. A core is a graph G for which all homomorphisms

G → G are automorphisms. The ”homomorphism-existence” relation induces a lattice on (the isomorphism classes of)

cores, which is the source of some particularly difficult problems. No algebra background is assumed.

Talk prerequisites: Elementary graph theory

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Representation Theory and Particle Physics

Clair Dai

Mathematical Physics (University of Waterloo)

The goal of this talk is to explore the close relationship between mathematics and theoretical physics. We will see

that, for great ideas to arise, math and physics must develop together with a common point of view. We will introduce

representations of Lie groups and Lie algebras through a few key examples and we will see how to draw weight diagrams.

We will talk about the complexified adjoint representation of SU(3), and how it connects to particle physics

Talk prerequisites: Linear Algebra

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An Introduction to the Single and Double-Exponential Sinc Collocation Method

Fatima Davelouis

Numerical Methods (University of Alberta)

We introduce the Sinc collocation method (SCM) combined with the single and double-exponential transformations

(SESCM and DESCM respectively). Compared to other methods, the SCM is robust, highly accurate, and its error

rate decays much faster as the number of collocation points increases. Overall, the SESCM and DESCM are powerful

tools that can be applied to solve many numerical problems in physics, chemistry and engineering. For instance, an

important application of the DESCM is to solve singular Sturm-Liouville eigenvalue problems, such as computing the

energy eigenvalues of quantum anharmonic oscillators, which have been studied as potentials in the Schrodinger equation.

In terms of methods, we numerically computed continuous functions and their Sinc approximation in Python. We compare

the accuracy of the DESCM vs. that of the SESCM.

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Representation theory of SL(2,R)

Stefan Dawydiak

Representation theory (University of British Columbia)

A representation of a group G is a G-action on a vector space. For finite dimensional vector spaces V , these correspond

to homomorphisms G → GL(V ). The classical statement of the Riesz-Fischer theorem is that a function [−π, π] → Rhas a Fourier series if and only if it is square-integrable. This can be restated by saying the regular representation

of the circle group, L2(T ), decomposes into one-dimensional subrepresentations corresponding to characters einx. We

19

will then consider certain representations of the non-compact group SL(2,R) which are “nice” when restricted to the

maximal compact subgroup SO(2,R). We will briefly discuss matrix coefficients of these representations, which generalize

matrix entries of finite-dimensional representations. These have interesting asymptotic expansions obtained by studying

differential equations, but might be attainable more immediately via model theory.

Talk prerequisites: Basic group theory, analysis, and linear algebra.

—————————————————————————————

An Introduction to RSA Encryption

Swapnil Daxini

RSA Encryption (University of Victoria)

Named after the three people who created it: Ronald Rivest, Adi Shamir and Leonard Adleman, RSA encryption was

originally introduced in 1977. It was one of the first practical asymmetric ciphers to be invented. Almost 40 years after

it was first introduced, it remains highly secure and is widely used for encrypted data transmission. The question is, for

how much longer will it remain secure? The first part of the presentation will focus on understanding the underlying

mathematical concepts of RSA. This would greatly help in identifying its strengths and weaknesses. To put in simple

words, the strength of RSA is based on the basic problem of factoring a multiple of prime numbers. This means that if

a faster method to factor numbers is discovered, RSA will no longer be secure. The second part of the presentation will

look into certain future developments in the field of science and math which would allow us to crack the RSA algorithm.

Talk prerequisites: Modular Arthimetic, Euler’s totient function, Euler’s Algorithm, Euler’s Theorem

—————————————————————————————

On Molecular Gases, and the Natural Numbers

Jacob Denson

Analysis / Dynamical Systems (University of Alberta)

All but the most schoolbook examples of dynamical systems remain beyond numerical solution; real world physical

situations involve the motion of millions of particles, yet the motion of three or more is intractable! Ergodic theory

gets around this by studying long term qualitative properties of such systems, avoiding the perils of numerical analysis.

Originally developed by Boltzmann to provide a mathematical foundation for statistical mechanics, the importance of

ergodic theory is now known to be widespread, and recently the theory has found surprising applications in number

theory; in this lecture, I introduce the central concepts of ergodicity, and apply these concepts to understand basic

asymptotic properties of the natural numbers.

Talk prerequisites: Multivariate Calculus, Elementary Knowledge of Differential Equations

—————————————————————————————

Quaternionic Exponentials and Possible Applications

Ayoub El Hanchi

Advanced Linear Algebra (Dawson College)

For n× n matrices A over C and z ∈ C, the equation exp(z(A− In)) = A, where In is the n× n identity matrix, has

applications in quantum physics. Motivated by this fact, we study quaternionic exponentials and exponentials of quaternion

matrices. We also look at some possible applications in quantum computation, as well as quaternionic quantum mechanics,

more specifically in the solution of the time dependent Schrodinger equation for physical systems whose states belong to

finite dimensional Hilbert spaces.

20

Talk Prerequisites: First year math

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An Introduction to Ramsey Theory on Graphs

Brandon Elford

Graph Theory and Combinatorics (Dalhousie University)

Have you ever been at a party and started thinking about math instead of socializing? Well you’re in the right place!

This talk will be an introduction to topics relating to Ramsey’s Theorem, the Pigeonhole Principle and The Classic Party

Problem (so you can at least think about parties while you’re at one!).

Talk prerequisites: Basic Graph Theory/ Combinatorics

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Exactly Solvable Potentials and Orthogonal Polynomials

Amir Farrag

Mathematical Physics (Dalhousie University)

The hermite polynomials which form an orthogonal set are solutions to the time independent schrodinger equation

representing particles in the quantum harmonic oscillator. It will be shown how Hermite’s differential equation can

represent the time independent schrodinger equation after undergoing a gauge transformation.It is found that exceptional

hermite polynomials represent the wavefunction of particles in potentials that are an extension of the quantum harmonic

oscillator. Such polynomials form a solution to the resulting Sturm-Luoisville eigenvalue problem and corresponding

energy levels of the particles are given by each eigenfunction’s eigenvalue.

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Symmetries of the Rayleigh Wave Equation

Sam Fisher

Partial Differential Equations (Dawson College)

A symmetry of a differential equation is a transformation on the space of (independent and dependent) coordinates

which maps each solution of the equation to another solution. The set of all continuous symmetries of a differential

equation forms a Lie group which is generated by the corresponding Lie algebra of infinitesimal symmetries. In this talk,

we determine the continuous symmetries of the Rayleigh wave equation and demonstrate how they can be used to obtain

new solutions from a given solution.

Talk prerequisites: First year math

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Recursive Graph Expansions of Feynman Diagrams

Seth Friesen

(Brandon University)

Feynman diagrams are of fundamental importance in particle physics. A given set of diagrams is related to the

probability of a specific physical process occurring and the lines and vertices in the diagrams have mathematical structure

related to the specific physical theory they represent. The calculated diagrams are an approximation, but can be expanded

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recursively in order to include more complicated diagrams. This increases the accuracy, as well as the difficulty of the

calculation. This talk will look at the way that these expansions are performed. It will include some techniques for

performing these calculations, focusing on recursive substitution and the reduction of the resulting diagrams.

Talk prerequisites: first-year calculus

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Geodesics

Gregorio Arturo Reyes Gonzalez

Differential Geometry (University of Waterloo - Instituto Tecnologico y de Estudios Superiores de Monterrey)

I will define geodesics on submanifolds of Euclidean space, describe their properties and give some non-common

examples.

Talk prerequisites: Calculus // Notion of Surfaces // Familiarity with vector fields along parametrized

curves

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Quantum Cryptography and the Key Rate Problem

Shouzhen Gu

Quantum Information (University of Waterloo)

The goal of cryptography is for two parties to communicate with each other without an adversary obtaining information

about the message. The security of classical schemes relies on the computational difficulty of solving certain mathematical

problems. However, if more advanced technology is developed, an eavesdropper may be able to decrypt the messages. In

this talk, I will describe how quantum mechanics can allow the two parties to generate a secret key that is secure by the

laws of physics. An important problem in quantum key distribution is to calculate the key rate, or efficiency, of different

protocols. In particular, I will share with you my research on an optimization problem to obtain lower bounds on the key

rate of arbitrary protocols.

Talk prerequisites: Any

—————————————————————————————

On the Chromatic Number of Latin Square Graphs

Laura Gutierrez Funderburk

Graph Theory (Simon Fraser University)

The chromatic number of a Latin square is the least number of partial transversals which cover its cells. This is just

the chromatic number of its associated Latin square graph. Although Latin square graphs have been widely studied as

strongly regular graphs, their chromatic numbers appeared to be unexplored. I present results by Nazli Besharati, Luis

Goddyn, E.S. Mahmoodian and M. Mortezaeefar on the chromatic number of a circulant Latin square, and the bounds

they found for some other classes of Latin squares. Furthermore, along with Dr. Goddyn we explore whether it is possible

to generalize bounds on the chromatic number of Cayley tables L = CAY (G) for all finite abelian groups G.

—————————————————————————————

22

Algorithmic and High Frequency Trading: The Mathematics of the Limit Order Book

Tyler Hofmeister

Mathematical Finance (University of Calgary)

Algorithmic trading refers to the use of programs and computers to generate and execute trades in markets with

electronic access. In recent years, studies have estimated that algorithmic trading makes up over a third of all trading

occurring in U.S. markets; this corresponds to over $13 trillion annually (USD). Algorithmic trading relies on High

Frequency trading data to in order to optimally execute trades. Using empirical High Frequency trading data, we introduce

the Limit Order Book (LOB) and Message data and show how these accurately describe the state of the market on a

millisecond to millisecond basis. After motivating an analytic model for the Limit Order Book, we discuss some of the

recent literature and probability models which have been used to model LOB dynamics.

Talk prerequisites: None

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A Brief Introduction to Bin Packing

Simon Huang

Optimization (University of Waterloo)

The bin packing problem is a classic problem of combinatorial optimization. Given a finite list of objects with weights,

how many identical bins of some fixed capacity are required to store them? The problem is NP-hard – in fact, simply

distinguishing whether 2 bins are sufficient is NP-hard. Nonetheless, there exist asymptotic polynomial-time approximation

schemes, which are close for large cases. We will give an overview of the bin packing problem, examine one such algorithm,

and discuss the history of research on this problem.

Talk prerequisites: (none)

—————————————————————————————

A Pathology in Analysis

Daniel Hudson

Analysis (University of Victoria)

There are many examples in mathematics that provide excellent arguments for the statement “obvious is the most

dangerous word in mathematics”. For example, the rationals are a countable, dense set in the reals, which are uncountable.

Moreover, the rationals have measure zero. Also, the Cantor function, also known as the “Devil’s Staircase”, is an increasing

function which is differentiable almost everywhere with zero derivative wherever it exists.

Surely, though, a function which is almost always unbounded must have infinite integral, right? The answer, despite

one’s most reasonable intuition, is no! In this talk, we will define a function which is unbounded almost everywhere, yet

has a finite (Lebesgue) integral.

Talk prerequisites: Calculus

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Analysis and Reconstruction of a Trace Norm Inequality

Aiden Huffman

Linear Algebra (University of Calgary)

23

We look at a result published by P. M. Alberti and A. Uhlmann (1978), where necessary and sufficient conditions are

given for the existence of a stochastic map, whose action simultaneously transforms two positive semi-definite matrices

with unit trace into two other ones. In our case we will only consider two-by-two matrices. Where we will show that their

main result can be rewritten using linear algebra and calculus into something surprisingly familiar.

Talk Prerequisites: Introductory Calculus and Linear Algebra

—————————————————————————————

Simplicial Homology and its Algorithmic Computation

Adam Humeniuk

Topological Data Analysis (University of Calgary)

Homology is an algebraic invariant of a topological space developed for the purpose of classifying spaces by identifying

unfilled holes or voids within. Homology is first defined for simplicial complexes which are topological spaces formed

as collections of simplices (sing. simplex), meaning points, edges, triangles, tetrahedra and their higher-dimensional

generalizations. I will introduce the homology of such spaces, called simplicial homology, and give a basic introduction

to its calculation. The first step in computing homology is to associate to such a complex a sequence of abelian groups;

thus, we foray into the realm of algebraic topology.

After computing the homology of some small complexes, we will see that it succeeds in identifying and counting their

holes. Having defined simplicial homology, I will show how its calculation can be reduced to the algorithmic reduction of

matrices.

Talk prerequisites: Algebra (groups and homomorphisms, matrices and linear algebra).

—————————————————————————————

Intersecting Sets in Two-Transitive Groups

Sam Jaques

Algebraic Graph Theory (University of Regina)

In a subgroup of Sym(n), two elements are said to intersect if they have the same action on some point, e.g., g(i) = h(i)

for some i. Given this definition, what’s the largest subset of a group such that any two elements intersect? This

is analogous to the Erdos-Ko-Rado (EKR) Theorem about intersecting sets, and I’ll use algebra, graph theory, and

representation theory to give some answers. Much like the EKR theorem, for 2-transitive sets one can find a maximal

intersecting set by taking the stabilizer of a point. But are there others?

Talk prerequisites: The Symmetric Group

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Public Key Exchange using Semidirect Products

Xinrui Jia

Cryptography (University of Waterloo)

A recent paper by Delaram Kahrobaei and Vladimir Shpilrain describes a key exchange protocol using a semidirect

product of groups/semigroups. We present the general protocol and the Diffie-Hellman key exchange as a special case of this

protocol. When implemented with a non-commutative group/semigroup, this key exchange by Kahrobaei and Shpilrain

can have advantages over Diffie-Hellman but care must be taken to avoid linear algebra attacks. Time permitting, we

discuss the analysis of the security of the protocol under certain semigroups and our approach to finding new suitable

semigroups. The authors suggest using a free nilpotent p-group to avoid these attacks.

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Talk prerequisites: Algebra, basic group theory

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Math and Comedy: An Unlikely Romance

Matthew Jordan

Math and Pop Culture (McMaster University)

There are 10 types of people in the world: those who understand binary, and 9 others.

Ever since there has been math, there has been mathematical comedy. You’re likely familiar with the worst of it (What’s

the integral of 1/cabin? Log cabin), but look past the groaners and you’ll discover that mathematicians have been behind

some incredibly sophisticated humor. Your favorite episode of The Simpsons was likely written by someone with a PhD

in math. You probably read xkcd or Saturday Morning Breakfast Cereal on a regular basis. You might know the satirist,

musician, and professor Tom Lehrer, whom Daniel Radcliffe once called “the funniest man of the 20th century.” In my

talk, I’ll be discussing a theorem that was proven in an episode of Futurama, sharing a few pieces from the Tom Lehrer

cannon, performing an original song, and throwing in a few groaners for good measure.

Talk prerequisites: None

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Sphere Packing, and the Baffling Properties of the E8 and Leech Lattices

Zachary Karry

Representation Theory (University of Toronto)

How many spheres can you fit into a space? What is the most efficient way to do it? These questions are the basis of

“Sphere Packing”, and the search for answers to these questions has lead to surprising applications in finite group theory,

physics, lie theory, fourier analysis, and even cryptography. In this talk we explore the basics of sphere packing, and the

extremely surprising properties of two particularly dense packings of spheres in 8 and 24 dimensions.

Talk prerequisites: High School for the basics, some example and applications will not be accessible to

everyone.

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A Really Gentle Introduction to EM: What it is and Why it’s Awesome

Nam-Hwui Kim

Statistics (University of Waterloo)

Estimating parameter values in statistics can be really messy: confusing derivatives, vectors and matrices, and the

sheer number of them to estimate, etc.. We realise - very quickly - that ML estimators rarely look pretty in any moderately

complicated situations. In light of this problem, the Expectation-Maximisation algorithm makes parameter estimation

much easier, thanks to the powerful computers at our disposal these days. By conditioning on the ”missing” data, the

algorithm provides an iterative maximisation of the expected value of the log-likelihood function of the parameters. This

idea of ”Whatever you don’t have, assume you have it and carry on” produces surprisingly stable ML estimates of the

parameters. This talk will introduce the rationale, procedure and an example (and hopefully more) to demonstrate the

algorithm’s usefulness in a very accessible way.

Talk prerequisites: Second year mathematics, including introductory probability and statistics

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25

Stone-Weierstrass by Functional Analysis

Taras Kolomatski

Analysis (University of Waterloo)

In a first real analysis course, the Stone-Weierstrass theorem is frequently proven by way of the Weierstrass Approx-

imation Theorem for polynomials. We can prove the theorem in many fewer lines and directly for general algebras of

continuous functions using ingredients from functional analysis. In this talk I will briefly recount the Krien-Milman The-

orem and the Riesz Representation Theorem for the dual of C(X), and then I will give a proof of Stone-Weierstrass that

is substantially easier to recall and recreate than the classic proof.

Talk prerequisites: Weak* topologies

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Phylogenetic Tree Construction using Computational Methods

Sean La

Bioinformatics (Simon Fraser University)

Phylogenetics is the study of the evolutionary relationships between groups of organisms, and a phylogenetic tree is

a diagram that graphically describes such relationships. Using methods in phylogenetics, scientists have been able to

reconstruct the genomes of ancient organisms which has applications in biological and epidemiological research. One

notable application in the reconstruction of the genome of the most recent common ancestor of a group of strains of

Mycobacterium tuberculosis complex originating from Beijing, China to study the origins of antibiotic resistance in this

organism. This bacteria is the cause of tuberculosis in humans and other organisms, and so further understanding of the

mechanisms behind antibiotic resistance would be a great boon for world health. In this talk I provide an overview of

the techniques involved in phylogenetics and ancestral reconstruction, with an emphasis on statistical and computational

methods such as Bayesian inference.

Talk prerequisites: Basic biology, statistics and computer science

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The Cone of Weighted Graphs Generated by Triangles

Haggai Liu

Combinatorics (University of Victoria)

We investigate the problem of classifying complete edge weighted graphs on n vertices indexed by [n] = {1, 2, . . . , n}where each triangle has a nonnegative weight. Such a graph G corresponds to a vector x with

(n2

)entries indexed by(

[n]2

). The vector, x, supports the cone of an inclusion matrix, W , of dimensions

(n2

)×(n3

), with rows indexed by

([n]2

)and columns indexed by the triangles,

([n]3

), of G. We wish to know whether or not x is a facet normal of this cone.

In particular, we are interested in determining which weighted graphs corresponding to a facet normal. We count the

equivalence classes of facet normals under graph isomorphism. To help with classifying facet normals, we present and

implement an algorithm allowing us to find a facet normal at random. We also relate the triangle decomposibility of

unweighted, undirected graphs to vectors in the cone of W .

Talk prerequisites: Second Year discrete math

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26

The Number of Degree d Curves Passing Through 3d− 1 Points in the Plane

Henry Liu

Geometry (University of Waterloo)

Through two points passes a unique line, an algebraic curve of degree 1; through five distinct points passes a unique

conic, an algebraic curve of degree 2. How many degree d algebraic curves pass through 3d-1 distinct points in the plane?

This innocuous question gets harder and harder to answer for increasing d. (Try to do d=3.) Following Kontsevich, we’ll

answer it in general by introducing and studying an object called the moduli space of stable maps. This approach to

such enumerative questions is known as Gromov-Witten theory, and has close ties with a result from string theory called

mirror symmetry, which I’ll outline if time permits.

Talk prerequisites: Intro course to algebraic geometry helpful, but not absolutely essential

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Exponentiation Methods for Ideals in Real Quadratic Fields

Reginald Lybbert

Computational Number Theory (University of Calgary)

The infrastructure of principal ideals in real quadratic fields has been proposed for use in a number of public-key

cryptosystems. The main cryptographic operation in this setting is the exponentiation of ideals. For this reason, we would

like to have fast algorithms for the exponentiation adapted to such ideals. There is a wide variety of exponentiation

algorithms in the literature; however, few have been adapted for this context. Currently, both binary and non-adjacent

form (NAF) have been implemented and analyzed in this context. In this presentation, other methods, including windowed-

NAF and double-base methods, will be analyzed. Also, some double exponentiation methods will be considered, such as

joint sparse form (JSF) and interleaving.

Talk prerequisites: A little number theory

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An Introduction to Continued Logarithms

Jason Lynch

Number Theory (University of Waterloo)

Like simple continued fractions, continued logarithms are a type of continued fraction that can be constructed through

a recursive process. Unlike simple continued fractions, continued logarithms have only been studied relatively recently.

This talk will give an overview of recent research into continued logarithms. We first focus on base 2 continued logarithms,

in which each term is a power of 2, giving some examples. We will see that many results for simple continued fractions have

analogues for base 2 continued logarithms. We then look at how to best extend to higher bases, and see the generalization

of the base 2 results. Finally, we will conclude with some interesting results about what happens when we let the base go

to infinity.

Talk prerequisites: Basic familiarity with continued fractions may be useful, but is not necessary.

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27

Talk About Math and Take Our Money: An Update from the CMS Student Committee

Kyle MacDonald

CMS Student Committee (McMaster University)

The Canadian Mathematical Society Student Committee (CMS Studc) exists to help develop the community of Cana-

dian mathematics students. Studc helps with funding and organization for CUMC, offers financial support for local and

regional student activities, and publishes Notes from the Margin, a semi-annual hodgepodge of student mathematical

writing. Come out to learn about writing for the Margin, organizing a conference, or generally getting involved with

Studc.

Talk prerequisites: None!

—————————————————————————————

Heat flow and Brownian motion

Kyle MacDonald

Analysis and statistical physics (McMaster University)

We derive a solution to the heat equation in the form of the expectation of a particular stochastic process known as

Brownian motion. Once we start to talk about expectations, we are motivated to ask which sets of paths count as events

in the associated probability space, and what the probability distribution looks like over the space of paths. By analogy

to the normal distribution on the real line, we construct a probability measure, known as Wiener measure, on simple

collections of paths. We discuss how this measure can be extended and used to derive elementary properties of Brownian

motion. We close by suggesting generalizations both to more complicated differential equations and to more complicated

stochastic process.

Talk Prerequisites: We presume elementary familiarity with random variables and differential equations,

but we do not assume advanced knowledge of PDE, stochastic processes, or physics.

—————————————————————————————

Partial Differential Equations and Population Dynamics

Kyle MacQuin

Partial Differential Equations (Dalhousie University)

The aim of this talk is to given the audience an idea on how partial differential equations are used to model ecological

population dynamics, particularly in aquatic species existing in an environment with drift. A mathematical model will be

derived using arguments involving conservation laws, and stochastic properties of the system. The conclusion will include

an analytic solution, and some computational results.

Talk prerequisites: Some PDEs background

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The Interchange Law, and the Eckmann-Hilton Argument

Roy Magen

Algebra (University of Toronto)

28

We often consider sets with operations, such as groups. Sometimes we also consider sets with multiple compatible

operations, such as rings, or algebras. We will look at a certain condition called the Interchange law, which looks roughly

like

(a1 � a2) ? (b1 � b2) = (a1 ? b1) � (a2 ? b2) or

(a1 a2

)(b1 b2

) =

((a1

b1

) (a2

b2

))

This induces some very surprising and impressive results, given by the Eckmann-Hilton argument, which can be seen

as a very intuitive result that arises from geometric intuition. We will also look at group objects for an application of this

result to provide a perspective on abelian groups and the nature of commutativity in general.

Talk prerequisites: Basic knowledge of group theory

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Why Some Sequences Are More Special Than Others

Calder Morton-Ferguson

Recursive sequences (University of Toronto)

In 1979, Douglas Hofstadter introduced the concept of a “meta-Fibonacci” sequence - a recursive sequence whose terms

depend on both the value and the position of its previous terms. In particular, Hofstadter’s “Q-sequence”, defined as Q(n)

= Q(n - Q(n - 1)) + Q(n - Q(n - 2)), has been particularly troublesome for mathematicians, and whether the sequence

is even defined for all n remains an open problem. In this talk, I investigate the Hofstadter-Huber class of sequences,

which was introduced in 1999 as a generalization of the Q-sequence, and explore the progress toward understanding these

sequences that has been achieved by Canadian mathematicians in the past decade. I then generalize the Hofstadter-Huber

class of sequences to an even larger class, and examine their often-predictable trends. When we conclude, it will be clear

that the inscrutably erratic behaviour of the Q-sequence makes it more special and perplexing than any other sequence

of its type.

Talk prerequisites: Familiarity with induction

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Orthogonality and Angular Measures in Normed Spaces

Michael Oliwa

Discrete Geometry (University of Calgary)

Angles and normality are fundamental concepts in Euclidean geometry. Unfortunately, they have no obvious analogues

in general normed spaces, which naturally arise in the study of convex bodies. Several generalized notions of orthogonality

have been introduced, all of which are equivalent in inner product spaces, but are otherwise distinct and have unexpected

properties. Important and perhaps the most intuitive definitions are those due to G. Birkhoff and R.C. James. Similarly,

there are many different ways to define an angle in normed planes, and they can serve different purposes. We will discuss

Birkhoff-James orthogonality and how to construct an angular measure with specific properties. In particular, we will go

over the contact number problem in the plane, where angular measures become vital.

Talk prerequisites: Real Analysis, Linear Algebra

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29

Continuing the Story (a Story of Analytic Continuation)

Adriano Pacifico

Analysis (University of Toronto)

In the study of calculus, the notion of regularity arises naturally in the sense that the “niceness” of a function can be

described by its smoothness. The more differentiable a function, the nicer it is. More precisely, regularity can be expressed

as the chain of inclusions C0 ⊃ C1 ⊃ . . . ⊃ C∞ ⊃ Cω . In particular, Cω, the class of analytic functions, is particularly nice

and among its good properties, we isolate one called analytic continuation and use this principle to try and find other

nice classes of functions. Departing from the familiar notions of regularity and the idea that an analytic function can be

expressed as its Taylor series approximation, we set out to continue this story with the power of analytic continuation.

Talk prerequisites: First year calculus and understanding the difference between a smooth and an

analytic function.

—————————————————————————————

Socialist Prime Numbers and a Composite Analogue

Sohraub Pazuki

Number Theory (Dalhousie University)

The idea of a socialist prime was first put forward by Erdos, and is only just beginning to see some results. A socialist

prime is a prime number p where 1!, 2!, 3!,..., (p-1)! are all distinct modulo p. We will explore a paper by Tim Trudgian

who puts forward some interesting results concerning where and how these numbers come up, and explore ways in which

we can create a composite analogue. We will do this by using Gauss’ generalization of Wilson’s Theorem and the concept

of a Gauss factorial to build the idea of so-called ’socialist composites’.

Talk prerequisites: Elementary Number Theory

—————————————————————————————

The Beurling- Gelfand Spectral Radius Formula

David Pechersky

Probability/Complex Analysis (University of Toronto)

The aim of this talk is to introduce the audience to some basic ideas in spectral theory. In particular, I’ll present

a pretty proof of the Beurling- Gelfand spectral radius formula, where functional and complex analysis show up in an

unexpected way.

Talk prerequisites: linear algebra, basic complex analysis, basic functional analysis

—————————————————————————————

Uncovering structure in data with persistent homology: Theory and Linguistic Ap-

plications

Matthew Pietrosanu

Statistics & Algebraic Topology (University of Alberta)

Persistent homology is a technique recently-developed in algebraic and computational topology well-suited for analysing

structure in complex, high-dimensional data. In this presentation, we discuss the significance and meaning of structure

30

and shape in data, and present persistent homology as a technique to recover the underlying topology of a dataset. We

give an introductory and intuitive overview of this method and, in particular, detail an application of persistent homology

to the analysis of associations between words of the English language.

Talk prerequisites: None!

—————————————————————————————

Simple is Elegant

Luke Polson

Physics (University of Victoria)

The purpose of the talk is to examine the set of consecutive side length right triangles with side lengths and hypotenuse

in the set of natural numbers. The triplets can be expressed as (a, a+1, c) where a and a+1 are side lengths and c is the

hypotenuse. For example, the first triplets in the sequence are (3, 4, 5), (20, 21, 29), and (119, 120, 169). Using a recursive

algorithm, the first term in each triplet can be determined (and thus subsequently the second and third terms). The only

previous (well-known) method to generate these triplets was a far more complicated method called Euclid’s formula. In

addition, taking the derivative of the recursive sequence (although it doesn’t intuitively make sense) tells us even more

about the sets of triplets.

Talk prerequisites: First Year Intro to Calc

—————————————————————————————

Does Mathematics Exist?

Guthrie Prentice

Physics (University of Victoria)

Max Tegmark proposes that the universe is an abstraction of a higher mathematical reality, much like the Pythagoreans

and the followers of Plato, whereas psychologists and Neuroscinetists like Rafael E. Nunez propose that mathematics is

all in the brain. Is there a testable hypothesis that might allow for both of these ideas to be true? This talk will cover

the latest explorations into both of these areas and a proposal for mathematics’ place in the universe that will hopefully

provide new avenues of research in mathematics and other fields.

Talk prerequisites: Introduction to First Year Calculus and Discrete Mathematics

—————————————————————————————

The No-three-in-line Problem

Zishen Qu

Combinatorics (University of Waterloo)

We discuss the no-three-in-line problem. The main open problem is presented, and related results are discussed. The

main problem is the following: For a n×n grid, what is the maximum number of points that can be placed with no three

points collinear? The main discussion will be on results of lower bounds on this number, and upper bound conjectures for

large n. Generalizations of the problem may be discussed.

Talk prerequisites: Vaguely understands the words analytic number theory, combinatorics

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31

How to Add Infinity to Infinity: The Arithmetic of Cardinal Numbers

Duncan Ramage

Set Theory (University of British Columbia)

In the nineteenth century, Georg Cantor began the study of cardinality and cardinal numbers by equating the size of

two sets with the existence of a bijection between them. Most everyone is familiar with the basic results of the subject,

that the power set of the natural numbers is equipollent with the real numbers, both of whose cardinality is greater than

that of the rational numbers and the natural numbers, both of which are again equipollent. However, generalizations of

these results are often left unexplored. In this talk, we will expand on these results, discussing the addition, multiplication,

and exponentiation of cardinal numbers in the context of ZFC and the generalized continuum hypothesis.

Talk prerequisites: Familiarity with aforementioned basic results

—————————————————————————————

The Firefighter Problem for All Orientations of the Hexagonal Grid

Shayla Redlin

Graph Theory (University of Victoria)

Let G be a directed graph in which, at time t = 0, a fire breaks out at vertex r. At each subsequent time, t = 1, 2, . . .

the firefighter defends d ≥ 1 undefended vertices which have not yet been reached by the fire, and then the fire spreads

from all vertices it has reached to all of their undefended out-neighbours. We show that, if G is an orientation of the

infinite hexagonal grid, then, by defending one vertex per time step, in a finite number of steps it is possible for the

firefighter to stop the fire from spreading beyond the vertices it has already reached.

Talk prerequisites: An interest in discrete mathematics!

—————————————————————————————

The Mathematics of Music

Lena Ruiz

Abstract Algebra (University of Victoria)

Musical patterns can be described with abstract algebra and graph theory. This presentation will introduce four of

the most important groups in musical group theory: the group of triadic transformations, the group of uniform triadic

transformations, the group of Riemannian uniform triadic transformations, and the group of transpositions and inversions.

Isomorphisms will be shown between these groups and a symmetric group, a dihedral group, and a wreath product.

We will also study a few musical graphs and their traversals, beginning with two dual toroidal graphs: the Waller’s

torus, whose vertices are chords, and its dual graph, the Tonnetz torus, whose vertices are notes. Finally, I will present

two of my own graphs: a combination of the two tori and a weighted digraph representing the most common sequences in

the standard classical repertoire.

Talk prerequisites: Introduction to algebra

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A Model of Bovine Babesiosis Including Juvenile Cattle

Chadi Saad-Roy

Mathematical Biology (University of Victoria)

32

In this talk, the transmission dynamics of Bovine Babesiosis, a tick-borne disease, will be explored. Bovine Babesiosis

(BB) is a tick-borne cattle disease caused by Babesia spp., which is found throughout the world and has massive economic

consequences. We formulate a model for the transmission of BB in cattle, and separate juvenile from adult cattle in our

formulation. Using parameter estimates from the literature, basic reproduction numbers are calculated and interpreted

biologically. Existence, uniqueness, and stability of equilibria present in this model will also be discussed. Numerical

simulations will be presented, and various control measures to control endemic BB in cattle populations are quantified.

Talk Prerequisites: Intro to differential Equations

—————————————————————————————

Linear programming: Theory and Applications

John Sardo

Combinatorial Optimization (University of Waterloo)

A whirlwind tour of the theory of linear programming and some interesting (real-world!) applications.

Talk prerequisites: Basic linear algebra

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Propositions as types as spaces

Daniel Satanove

Homotopy Type Theory (University of British Columbia)

One can think of sets as discrete spaces. Can we have a foundation of math built on more general spaces? That is

what happens in homotopy type theory. Sets become only one sort of type, with groupoids and higher groupoids being the

more connected spaces. There is an extra feature that in type theory, propositions are also types which can be thought of

the collection of their proofs. I will give a Rosetta Stone for the three perspectives on HoTT: logical, type theoretic, and

topological.

Talk prerequisites: Logic

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Syzygies and Betti Tables, a Taste of Computational Algebra

Aaron Slobodin

Computational Algebra (Quest University Canada)

I will discuss some of the basic concepts in computational algebra, including polynomial rings, syzygies, and Betti

tables. Syzygies express a specific relationship between different sets and are fundamental objects in many fields of

mathematics. The analysis of strings of syzygies, compactly expressed in Betti tables, can uncover deep relationships and

patterns. I hope to unmask the jargoned term “syzygy” and expose its simplicity and application, while sharing some of

the patterns I have found in Betti tables this summer during my research. My talk is aimed at a general mathematics

audience.

Talk prerequisites: Familiar with polynomials.

—————————————————————————————

33

Classifying Leafsets and Determining Existence of Opposite Trees

Mariia Sobchuk

Graph Theory (University of Waterloo)

Kathie Cameron and I are working on problems of characterizing the sets of vertices of a graph are the set of leaves of

a spanning tree as well as of the existence of opposite spanning trees, defined as follows. If G is a graph whose vertices are

labelled, then T and T’ are opposite trees if for each vertex u of G, the degree of u in T is different from its degree in T’.

An approach developed by Cameron and Sands involved the interchange of leaves and non-leaves. They concluded that all

spanning trees in Kn have an opposite tree, unless T is a star, and that all trees in Knn have an opposite tree for nontrivial

cases. Cameron and Kalanda proved that the existence of an opposite tree is NP-complete. For Kmn (n > m > 1) we

proved that an opposite tree exists iff the number of leafs in the larger coclique is at most m-1. In this talk I will discuss

some properties of leafsets and opposite trees and describe the results in greater detail.

Talk Prerequisites: Basic Graph Theory (definitions, trees)

—————————————————————————————

Drawings of Complete Graphs

Matthew Sunohara

Topological Graph Theory (University of Toronto)

It is well known a complete graph on five or more vertices is non-planar, i.e. any drawing of it in the plane has some

edges that cross each other. The crossing number cr(Kn) of the complete graph on n vertices is the minimum number of

crossings in a (good) drawing of Kn. In the early 1960s Harary and Hill conjectured that cr(Kn) = 14b

n2 cb

n−12 cb

n−22 cb

n−32 c;

this has only been verified for n ≤ 12. There are a number of variations on the crossing number that are obtained by

restricting the kinds of drawings that are allowed. For example, the rectilinear crossing number, where edges must be

straight line segments. In this talk we will discuss crossing numbers and the different kinds of graph drawings that have

been motivated by the study of cr(Kn).

Talk prerequisites: Basic graph theory and topology

—————————————————————————————

Representations and Characters of finite groups

Bowen(Coco) Tian

Representation Theory of Finite Groups (University of Alberta )

Representations of finite groups give us a way of visualizing a group G as a group of matrices. A representation is a

homomorphism from G into a group of invertible matrices. I will define group representations and group algebras first.

Then I will introduce the concept of CG-modules and show the proof of Shur’s Lemma and its immediate consequence

regarding irreducible representations of finite abelian groups. Next I will demonstrate some basic properties and results

of character theory, including orthogonality relations and induced characters. To illustrate the use of character table, I

will give an example of calculating charater table.

Talk prerequisites: group theory and linear algebra

—————————————————————————————

34

Schur-Positivity of Equitable Ribbons

Foster Tom

Algebraic Combinatorics (University of British Columbia)

Schur functions form an important basis for the space of symmetric functions and show up in areas from representation

theory to quantum mechanics. Given an appropriate diagram of boxes, we construct its corresponding Schur function by

counting the numbers of tableaux: fillings of these boxes with integers that satisfy some simple conditions. We then form

the Schur-positivity partially ordered set by comparing these numbers of tableaux. In this talk, we present some new

results of how order relations in this partially ordered set can be derived from properties of the diagrams.

Talk prerequisites: Nothing

—————————————————————————————

Investigating the Stability of Disease Models with Temporary Immunity

Chelsea Uggenti

Mathematical Biology (University of Waterloo)

This presentation explores the stability of a disease model with three recovered classes, which has two equilibria: a

disease-free equilibrium and an endemic equilibrium. The stability of the disease- free equilibrium is straight-forward

to understand by using certain theorems related to the basic reproduction number R0. The stability of the endemic

equilibrium is more difficult. To study it, I first simplify the model in order to understand which parts of the parameter

space result in an unstable endemic equilibrium. Using this, I then return to the original model, showing that it is possible

to have an unstable endemic equilibrium co-existing with a periodic orbit.

Talk prerequisites: Second or Third Year Intro to Math Bio

—————————————————————————————

Bounding Polynomial Roots using Matrix Norms

Trevor Vanderwoerd

(Redeemer University College)

Due to their importance in many areas of mathematics and science, the roots of polynomials have attracted significant

interest. This interest has resulted in techniques for finding exact and numerical solutions, and in bounds on the roots.

One of the earliest and most basic bounds is the Cauchy bound, which states that the modulus of each root is less than

1+max {|ai|}, for the polynomial pn(x) = xn+an−1xn−1 + · · ·+a2x

2 +a1x1 +a0. This bound arises from applying matrix

norms to the Frobenius companion matrix. In recent years, mathematicians, including undergraduate students, have

found new forms of companion matrices. Following these discoveries, the properties of the new companion matrices were

explored to determine their suitability for more accurate bounds. In certain cases, the Cauchy bound can be significantly

improved on. For those interested in undergraduate research, the subject matter of this talk has largely been developed

by undergraduate students, including the speaker.

Talk prerequisites: an introductory course in Linear Algebra.

—————————————————————————————

35

Planar Maps and the Largest Face-degree

Koen van Greevenbroek

Combinatorics (Simon Fraser University)

This talk will be about the combinatorial toolbox, packed to the brim with bijections, and how to apply these tools

to a problem on planar maps. Planar maps are rooted planar graphs endowed with an embedding, and are extensively

studied in combinatorics. One of the things we are interested in is what a typical (uniformly randomly drawn) planar map

looks like. In particular, we will study the expected degree of the largest face in a typical planar map, when we fix the

number of edges and faces. To this end, we put the planar maps in bijection with a type of labelled binary strings, such

that faces map to runs of 0s. With the appropriate approximations, we are able to model the binary strings, and find an

asymptotic expression for the expected degree of the largest face in a map with n edges and nα faces.

Talk prerequisites: Basic graph theory

—————————————————————————————

Optimal Course Scheduling

Liam Wrubleski

Optimization (University of Calgary)

Scheduling and assigning courses is a task that must be performed in every department of every university, every

semester. In fact, this task must be performed any time multiple events must be scheduled in the same timeframe, so

establishing an efficient method of performing this task is extremely desirable. In this presentation, I will talk about how

we have developed a model that solves this to optimality extremely quickly, using free and open source software.

Talk prerequisites: None

—————————————————————————————

Bounding Symmetry in Colour

Ethan White

Graph Theory (University of Calgary)

A graph consists of a set of vertices (points) and a set of edges (line segments connecting pairs of points), and a

colouring of a graph is a labeling of its vertices with colours such than any two vertices connected by an edge have

different colours. The challenge is to find the fewest number of colours needed to colour a graph. Graph colouring has

a long history going back to the Four Colour Conjecture (now the Four Colour Theorem) first posed in 1852. A recent

variation on graph colouring involves colouring a graph in such a way that all the symmetries of the graph are destroyed.

Such a colouring is called a distinguishing colouring of a graph, and the fewest number of colours needed to accomplish

this is called the graph’s distinguishing chromatic number. The Nordhaus-Gaddum Theorem links the chromatic number

of a graph to that of its complement. In my talk, an analogue of this theorem for a graph’s distinguishing chromatic

number will be discussed.

Talk prerequisites: None

—————————————————————————————

36

The Chromatic Number of the Plane and the Axiom of Choice

Angela Wu

Geometry (University of Toronto)

How many colours does it take to colour the plane such that any two points distance 1 apart are different colours?

More than 4, at most seven, and the answer probably depends on the axiom of choice!

Talk prerequisites: Know what an axiom is, and what a graph is. Familiarity with measure is helpful but

not necessary.

—————————————————————————————

The Robinson-Schensted-Knuth Correspondence

Shelley Wu

Algebraic Combinatorics (University of Waterloo)

In representation theory, there is an association between all the irreducible representations of Sn and all the partitions

λ of n. Moreover, the set of Standard Young Tableau of shape λ forms a basis to the representation that corresponds to λ.

Denote the cardinality of such set with fλ. Then following from the dimensionality theorem,∑λ`n(fλ)2 = n!. Neglecting

its genesis, this has a combinatorial interpretation, namely a bijection between (P,Q), pairs of Standard Young Tableau

of the same shape, and elements σ in Sn. What is in common between elements in Sn with the same P? What does the

shape of P tell us about σ? If we tweak σ, how is the change reflected in the image of the bijection? We will investigate

the properties of the bijection and answer these questions. In the end, I will introduce the Hook Length Formula, which

is a probabilistic approach to compute f !λ.

Talk prerequisites: Any

—————————————————————————————

Things I learned about Gauss-Bonnet

Mengxue Yang

Differential Geometry (University of Waterloo)

The Gauss-Bonnet theorem is an important theorem in the differential geometry of surfaces. Its statement is easy to

understand informally; it says that the overall geometry of a surface is related to the topology of the surface. In particular,

we can establish an equality involving the integral of the Gaussian curvature and the Euler characteristic for a surface.

This is surprising and has many consequences. This presentation aims to explain Gauss-Bonnet in more details and also

give examples of its application.

Talk prerequisites: Intro to differential geometry

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Riemannian Geometry

Yuan Yao

Geometry/physics (University of Toronto)

The goal of this talk will be to introduce you to Riemannian geometry. I will start with the definitions of basic relevant

objects, Riemannian manifolds, connections, parallel transport, geodesics and curvature. Then I will discuss some more

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interesting classical results that relate the curvature of the manifold to its topology, for example ”classification” of spaces

of constant curvature and the celebrated Sphere theorem. If time allows I will finish by drawing a smiley face on the

board.

Talk prerequisites: manifolds, vector bundles, tensors- essential. lie bracket, covering spaces-would help

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Quantum Games - When Classical Games just Aren’t Enough

Guo Xian Yau

Game Theory/Quantum Information Theory (University of Waterloo)

It is known that many classical cooperative games have no winning strategies for the players. When Alice and Bob is

separated in different rooms where no physical communication is available, winning against the odd is merely a game of

chance. This situation is changed if we allow quantum interractions between Alice and Bob; by measuring pairs of highly

entangled state particles, Alice and Bob can have a winning strategy for the cooperative game. In this talk, I will talk

about a specific setting for the game - the Mermin Magic Square game. If time permits, I will also present how these

games are related to graphs.

Talk prerequisites: Know how to draw n by n grid and at least 2 geometrical objects.

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Life Insurance: From Zootopia to Reality

Yan Zhang

Actuarial Science (University of Waterloo)

An actuary is a business professional who analyzes the financial consequences of risk. In the life insurance industry, they

work in the Pricing, Valuation, Asset Liability Management and Corporate departments. In particular, pricing actuaries

design products that balance expected profitability and market competitiveness. In this talk, I will touch on actuarial

science and its role in life insurance, specifically pricing. Most importantly, I will explain how insurance companies use

statistics and financial theory to determine premiums charged. If time permits, I will also discuss Universal Life, which is

a popular yet complicated type of life insurance.

Talk prerequisites: N/A

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An Introduction to Non-Standard Calculus

Reila Zheng

Calculus (University of Waterloo)

In this talk I will present a brief overview of non-standard calculus. I will define the algebra of hyperreal numbers.

Using this background I will present a few simple theorems under this theory, theorems that you may see in a first year

standard calculus course.

Talk Prerequisites: First year calculus

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Markov Chains and n-dimensional Lattice Random Walks

Kevin Zhou

Statistics (University of Waterloo)

Consider a drunk man who lives in a (2-dimensional) city where both his home and his favourite bar are located at

the origin. Along each integer valued coordinate in the city is a road, dividing the city into a lattice of square blocks.

One day, the drunk man exits the bar, picks one of the four directions at random, and heads in that direction until he

reaches the next intersection. He picks a random direction again at the next intersection (including the direction he came

from), and so on. Will the drunk man eventually reach his house? This is an interesting question whose general answer in

n-dimensions can be easily answered using the theory of Markov Chains. As we shall see, there are values of n for which

the drunk man has a positive probability of NEVER returning to his house! Conclusion: be careful the next time you

decide to drink in a multi-dimensional bar!

Talk prerequisites: Basic probability

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Finite Mixtures of Nonparametric Regression Models with Generalized Additive Com-

ponents

Robert Zimmerman

Statistics (University of Waterloo)

The fitting of classical regression models to data can be disastrous when the model has been misspecified or the data

is heterogeneous (i.e., several different subsets of the data follow their own distinct distributions). Finite mixtures of

regression models, which collect separate parametric regression models (one for each group) into a convex combination,

have been recently generalized to nonparametric models whose component functions are estimated via kernel smoothing.

However, such multivariate kernel smoothing suffers from the ”curse of dimensionality”; thus generalized additive models

(GAMs) for function estimation have been developed as a practical alternative. In this talk, we build up towards the class

of finite mixtures of regression models with generalized additive components by first reviewing basic regression models,

and then introducing the concepts of finite mixture models, nonparametric models, and GAMs.

Talk prerequisites: First Year Statistics (Linear Regression)

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The Class Group and Ideal Numbers

Alexandre Zotine

Algebraic Geometry (Simon Fraser University)

An introduction to algebraic number theory, integral extensions and classifications of rings of integers using the class

group. Includes a discussion on the origin of the term ideal, and a proof that 26 is the unique non-zero integer directly

between a perfect square and perfect cube.

Talk prerequisites: Introductory Ring Theory, Groups

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5 Sponsors

Thank you to all of the following organizations for their generous sponsorship of CUMC 2016:

Merci a toutes les organisations suivantes pour leur soutien geneereux du CCEM 2016:

• University of Victoria Student Society

• University of Victoria Department of Mathematics

and Statistics

• The Fields Institute for Research in Mathematical Sci-

ences

• University of Victoria Faculty of Science

• Canadian Applied and Industrial Mathematics Society

• Maplesoft

• Statistical Society of Canada

• Pacific Institute for the Mathematical Sciences

• Canadian Institute of Actuaries

• Centre de Recherches Mathematiques

• YYJ Airport Shuttle

• Monk Office Supplies

• Communications Security Establishment Canada

• Westcoast Women in Engineering, Science, and Tech-

nology

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6 Contacts

6.1 Conference Contacts

If you have any questions or concerns during CUMC 2016, feel free to ask any volunteer, or contact us via:

Si vous avez des questions ou des preoccupations durant CCEM, n’hesitez pas a demander aux volontaires ou vous pouvez

nous contacter au moyen d’une de ces modes:

• E-mail: cumc@cumc.math.ca

• Facebook: facebook.com/CUMC2016CCEM/

• Twitter: @CUMC2016

6.2 Emergency Contacts

In case of emergency:

En cas d’urgence:

• Fire/Police/Ambulance: 9-1-1

• Campus Security: 250-721-7599

• Emergency Updates: @uvicemerg or 250-721-8620

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