NEAM 2 - University at Albany, SUNYmb533919/NEAM 2017 abstracts.pdf · 2017-10-13 · NEAM 2...

NEAM 2

NortheasternAnalysisMeeting

AlbanyNew York

October 13 - 15, 2017

Organizers:

Marius Beceanu, University at Albany, SUNYJoshua Isralowitz, University at Albany, SUNYRongwei Yang, University at Albany, SUNY

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NEAM 2

Friday October 13

On Friday morning, the conference packet pickup, the coffee breaks, and the early morningcoffee and snacks are between Lecture Center 19 and Lecture Center 20.

8:15 - 9:00 Conference packet pickup / coffee / snacks

Lecture Center 20:

8:30 - 9:00 Addresses by the CAS Dean, Chair, and organizers9:00 - 9:40 Monica Visan, UCLAAlmost sure scattering for the cubic NLS in four dimensions9:50 - 10:30 Murat Akman, University of ConnecticutA Minkowski problem for nonlinear capacity

Coffee break

11:00 - 11:40 Stefanie Petermichl, University of ToulouseOn the matrix A2 conjecture11:50 - 12:30 Lewis Coburn, University at Buffalo, SUNYToeplitz quantization

Lunch

2:45-4:00 Parallel sessionsCoffee break near Lecture Center 44:30-7:00 Parallel sessions

Friday Parallel Session 1 is in Lecture Center 4Friday Parallel Session 2 is in Lecture Center 5Friday Parallel Session 3 is in Lecture Center 6

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The Friday afternoon conference packet pickup and the coffee breaks are in the LectureCenter corridor, near Lecture Center 4 and Argos Tea.

Friday Parallel Session 1

2:45 - 3:05 Josh Brummer, Kansas State UniversityBilinear operators with homogeneous symbols, smooth molecules, and Kato-Ponce inequalities3:10 - 3:30 Dong Dong, University of Illinois at Urbana-ChampaignHilbert transforms in a 3 by 3 matrix3:35 - 3:55 Gennady Uraltsev, Cornell UniversityUniform bounds for the bilinear Hilbert transform

4:00 - 4:30 Coffee break

4:30 - 4:50 Almaz Butaev, Concordia UniversitySome refinements of the embedding of critical Sobolev spaces into BMO4:55 - 5:15 Cezar Lupu, University of PittsburghAnalytic aspects in the evaluation of multiple zeta values and multiple Hurwitz zeta values


2:45 - 3:05 A. Shadi Tahvildar-Zadeh, Rutgers UniversityGeneral Relativity at the Atomic Scale3:10 - 3:30 Timur Akhunov, State University of New York, BinghamtonWhen is Laplacian too degenerate to be laplacian?3:35 - 3:55 Zhenfu Wang, University of PennsylvaniaQuantitative estimates of propagation of chaos for stochastic systems with W−1,∞ kernel


4:30 - 4:50 Walton Green, Clemson UniversityHarmonic analysis proof of the boundary observability for the wave equation4:55 - 5:15 Dawit Habte Gebre, University of L’AquilaAnalysis of turbulent hydromagnetic flow with radiative heat over a moving vertical plate ina rotating system5:20 - 5:40 Marius Beceanu, University at Albany, SUNYNew methods for the study of supercritical wave equations

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5:45 - 6:05 Petr Siegl, University of Bern, SwitzerlandNon-accretive Schrodinger operators and exponential decay of their eigenfunctions6:10 - 6:30 Jack Arbunich, University of Illinois at ChicagoRegularizing nonlinear Schrodinger equations through partial off-axis variations.6:35 - 6:55 Yunyun Yang, University of West Virginia, Institute of TechnologySome subtleties in the relationships among heat kernel invariants, eigenvalue distributions,and quantum vacuum energy


2:45 - 3:05 Meredith Sargent, Washington University in St. LouisCarlson’s theorem for different measures3:10 - 3:30 Ievgen Bilokopytov, University of ManitobaContinuity and holomorphicity of symbols of weighted composition operators3:35 - 3:55 Hugo J. Woerdeman, Drexel UniversityComplete spectral sets and numerical range


4:30 - 4:50 Miron Bekker, University of Pittsburgh at JohnstownOn roots of determinant of one class of holomorphic matrix-valued functions4:55 - 5:15 Kathryn McCormick, University of IowaRiemann surfaces, holomorphic bundles, and boundary representations5:20 - 5:40 Bhupendra Paudyal, Central State UniversityThe lattices of invariant subspaces of a class of operators on the Hardy space5:45 - 6:05 Benjamin Russo, University of ConnecticutA generalization of the Fock space6:10 - 6:30 Raffael Hagger, Leibniz University HannoverCompactness and essential spectra on bounded symmetric domains6:35 - 6:55 Roozbeh Gharakhloo, Indiana UniversityOn the asymptotics of Toeplitz+Hankel determinants

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NEAM 2

Saturday October 14

The conference packet pickup, coffee breaks, and the early morning coffee and snacks are inthe Lecture Center corridor, near Lecture Center 4 and Argos Tea.


Lecture Center 4:

9:00 - 9:40 Daniel Tataru, UC BerkeleyEnergy-critical Yang–Mills9:50 - 10:30 Ben Dodson, Johns Hopkins UniversityGlobal well-posedness and scattering for the cubic wave equation in three dimensions

Coffee break

11:00 - 11:40 Guihua Gong, University of Puerto RicoOn the classification of unital simple separable nuclear C∗-algebras11:50 - 12:30 Mihai Putinar, UC Santa BarbaraPositivity transformers

Lunch

2:10 - 2:50 Eric Sawyer, McMaster UniversityA two weight local Tb theorem for the Hilbert transform.

3:00-3:50 Parallel sessionsCoffee break4:20-6:50 Parallel sessions

Saturday Parallel Session 1 is in Lecture Center 4Saturday Parallel Session 2 is in Lecture Center 5Saturday Parallel Session 3 is in Lecture Center 6

7:15 Banquet: Patroon Room, Campus Center

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Saturday Parallel Session 1

3:00 - 3:20 Azita Mayeli, City University of New York, Queensborough and the GraduateCenterOrthogonal Gabor bases on finite vector spaces3:25 - 3:45 Pablo Jimenez-Rodriguez, Kent State UniversityOn some trivial (and not so trivial) inequalities for convex functions.


4:20 - 4:40 Mihai Stoiciu, Williams CollegeBounds for the pseudospectra of various classes of matrices and operators4:45 - 5:05 Gabriel Prajitura, State University of New York BrockportLinear Chaos5:10 - 5:30 Anca Radulescu, State University of New York at New PaltzTemplate iterations of quadratic maps and hybrid Mandelbrot sets5:35 - 5:55 Tyler Bongers, Michigan State UniversityStretching and rotation sets of quasiconformal maps6:00 - 6:20 Lawrence Fialkow, SUNY New PaltzThe core variey of a multisequence in the truncated moment problem6:25 - 6:45 Ivana Alexandrova, University at Albany, SUNYSemi-Classical-Fourier-Integral-Operator-Valued pseudodifferential operators and scatteringin a strong magnetic field


3:00 - 3:20 Manki Cho, Rochester Institute of TechnologySteklov eigenproblems and representations of electrostatics approximations of vector fields3:25 - 3:45 Lev Sakhnovich,The generalized scattering problems, ergodic type theorems


4:20 - 4:40 Ebru Toprak, University of Illinois at Urbana ChampaignDispersive estimates for massive Dirac operators4:45 - 5:05 Razvan Teodorescu, University of South FloridaStochastic regularization of singularities in free boundary problems5:10 - 5:30 Xueying Yu, University of Massachusetts AmherstGlobal well-posedness and scattering for the quintic NLS in two dimensions5:35 - 5:55 Andrei Tarfulea, University of ChicagoImproved estimates for thermal fluid equations

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6:00 - 6:20 Mengxia Dong, University of ConnecticutExistence of extremal functions for higher order derivatives Caffarelli-Kohn-Nirenberg in-equalities6:25 - 6:45 Jungang Li, University of ConnecticutConcentration-compactness principles on the Heisenberg group and Riemannian manifolds


3:00 - 3:20 Javad Mashreghi, Laval UniversitySome Preserver theorems in Hp Spaces3:25 - 3:45 Pan Ma, Central South University (China)Compactness of Toeplitz operators and Hankel operators on model spaces


4:20 - 4:40 Muhammed A. Alan, Syracuse UniversityWeighted polynomial hulls4:45 - 5:05 Arthur Parzygnat, University of ConnecticutCategories in Probability5:10 - 5:30 Ruhan Zhao, State University of New York, BrockportOn Berezin type operators and Toeplitz operators5:35 - 5:55 Hyun Kyoung Kwon, University of AlabamaOn the similarity of Cowen-Douglas operators6:00 - 6:20 Jianchao Wu, Penn State UniversityNoncommutative dimensions and crossed product C∗-algebras.6:25 - 6:45 Qijun Tan, Penn State UniversityAsymptotic containment of representations and the spherical Plancherel formula.

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NEAM 2

Sunday, October 15

The conference packet pickup, coffee breaks, and the early morning coffee and snacks are inthe Lecture Center corridor, near Lecture Center 4 and Argos Tea.


Lecture Center 4

9:00 - 9:40 Raul Curto, University at IowaToral and spherical Aluthge transforms9:50 - 10:30 Wilhelm Schlag, University of ChicagoStructure theorems for intertwining wave operators in three dimensions

Coffee break

11:00 - 11:40 Sergei Treil, Brown UniversityFinite rank perturbations, Clark model, and matrix weights11:50 - 12:30 Francesco Di Plinio, University of VirginiaMaximal averages and singular integrals along vector fields in higher dimension

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Abstracts

Timur AkhunovState University of New York, [email protected]: When is Laplacian too degenerate to be Laplacian?Abstract: Solutions of laplacian are smooth, right? If you allow variable coefficients, smooth-ness of the coefficients becomes an obstacle to unlimited smoothness. If the coefficients aredegenerate things can go wrong more dramatically. Come find out more.

Murat AkmanUniversity of [email protected]: A Minkowski problem for nonlinear capacityAbstract: The classical Minkowski problem consists in finding a convex polyhedron fromdata consisting of normals to their faces and their surface areas. In the smooth case, thecorresponding problem for convex bodies is to find the convex body given the Gauss curvatureof its boundary, as a function of the unit normal. The proof consists of three parts: existence,uniqueness and regularity.In this talk, we study a Minkowski problem for certain measure associated with a compactconvex set E with nonempty interior and its A-harmonic capacitary function in the comple-ment of E. Here A-harmonic PDE is a non-linear elliptic PDE whose structure is modeledon the p-Laplace equation. If µE denotes this measure, then the Minkowski problem weconsider in this setting is that; for a given finite Borel measure µ on Sn−1, find necessaryand sufficient conditions for which there exists E as above with µE = µ. We will discuss theexistence, uniqueness, and regularity of this problem in this setting.

Muhammed A. AlanSyracuse [email protected]: Weighted polynomial hullsAbstract: Regularity of a compact set is important in Pluripotential theory, Approximationtheory and Separately analytic functions. Recently Sadullaev introduced weighted regular-ity notions. In this talk, we will discuss the Weighted local and global Pluriregularity, andsupports of weighted equilibrium measures.

Ivana AlexandrovaUniversity at Albany, [email protected]: Semi-Classical-Fourier-Integral-Operator-Valued Pseudodifferential Operators and Scat-tering in a Strong Magnetic Field

mailto:[email protected]




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Abstract: We analyze the microlocal structure of the semi-classical scattering amplitude forSchrodinger operators with a strong magnetic and a strong electric fields at non-trappingenergies. For this purpose we develop a framework and establish some of the properties ofsemi-classical-Fourier-integral-operator-valued pseudodifferential operators and prove thatthe scattering amplitude is given by such an operator.

Jack ArbunichUniversity of Illinois [email protected]: Regularizing nonlinear Schrodinger equations through partial off-axis variationsAbstract: We study a class of (focusing) nonlinear Schrodinger-type equations derived re-cently by Dumas, Lannes and Szeftel within the mathematical description of high intensitylaser beams. These equations incorporate the possibility of a (partial) off-axis variation ofthe group velocity of such laser beams through a second order partial differential operatoracting in some, but not necessarily all, spatial directions. We study the well-posedness the-ory for such models and obtain a regularizing effect, even in the case of only partial off-axisdependence.

Marius BeceanuUniversity at Albany, [email protected]: New methods for the study of supercritical wave equationsAbstract: In this talk I shall present some new methods for the study of energy-supercriticalevolution equations and their applications.

Miron BekkerUniversity of Pittsburgh at [email protected]: On roots of determinant of one class of holomorphic matrix-valued functionsAbstract: We consider holomorphic in the unit disk matrix-valued functions with entries inthe Nevanlinna class of functions of bounded characteristic. For the roots zj, j = 1, 2, . . .,zj 6= 0 we give estimates for

∑(|zj|−1 − 1) and [

∑(|zj|−1 − 1)2]1/2.

Ievgen BilokopytovUniversity of [email protected]: Continuity and Holomorphicity of Symbols of Weighted Composition OperatorsAbstract: We consider the following problem: if F and E are (general) normed spaces ofcontinuous functions over topological spaces X and Y respectively, and ω : Y → C andΦ : Y → X are such that the weighted composition operator WΦ,ω is continuous, when canwe guarantee that both Φ and ω are continuous? An analogous problem is also consideredin the context of normed spaces of holomorphic functions.





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Tyler BongersMichigan State [email protected]: Stretching and Rotation Sets of Quasiconformal MapsAbstract: Quasiconformal maps in the plane are orientation preserving homeomorphismsthat satisfy certain distortion inequalities; infinitesimally, they map circles to ellipses ofbounded eccentricity. Such maps have many useful geometric distortion properties. In thiswork, we study the size of the sets where a quasiconformal map can exhibit given stretchingand rotation behavior. We improve results by Astala-Iwaniec-Prause-Saksman and Hitruhinto give examples of stretching and rotation sets with non-sigma-finite measure at the appro-priate Hausdorff dimension.

Josh BrummerKansas State [email protected]: Bilinear Operators with Homogeneous Symbols, Smooth Molecules, and Kato-PonceInequalitiesAbstract: We present a unifying approach to establish mapping properties for bilinear pseu-dodifferential operators with homogeneous symbols in the settings of function spaces thatadmit a discrete transform and molecular decompositions in the sense of Frazier and Jawerth.As an application, we obtain related Kato-Ponce inequalities. This is a joint collaborationwith Virginia Naibo.

Almaz ButaevConcordia UniversityTitle: Some refinements of the embedding of critical Sobolev spaces into BMOAbstract: In 2004, Van Schaftinen showed that the inequalities established by Bourgainand Brezis give rise to new function spaces that refine the classical embedding W 1,n(Rn) ⊂BMO(Rn). In this talk, we discuss the non-homogeneous analogs of these function spaceson Rn and their generalizations to Riemannian manifolds with bounded geometry.

Manki ChoRochester Institute of [email protected]: Steklov eigenproblems and representations of electrostatics approximations of vectorfields Abstract: This talk will discuss expressions for the boundary potential that providesthe Steklov approximation of the electrostatic potential on a bounded region. The boundarypotential is found by using a special basis of the trace space for the space of allowable poten-tials. The trace space is described by its representations with respect to a basis of Stekloveigenfunctions. Error estimates for approximations of electrostatic potential on planar re-gions by the trace space will be discussed. Numerical results will be presented.

Lewis Coburn




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University at Buffalo, State University of New [email protected]: Toeplitz quantizationAbstract: I discuss some recent work with Wolfram Bauer and Raffael Hagger. Here, Cn

is complex n-space and, for z ∈ Cn, we consider the standard family of Gaussian measuresdµt(z) = (4πt)−n exp(−|z|2/4t)dv(z), t > 0 where dv is Lebesgue measure. We considerthe Hilbert space L2

t of all dµt-square integrable complex-valued measurable functions on Cn

and the closed subspace of all square-integrable entire functions, H2t . For f measurable and

h ∈ H2t with fh ∈ L2

t , we consider the Toeplitz operators T(t)f h = P (t)(fh) where P (t) is the

orthogonal projection from L2t onto H2

t . For f bounded (f ∈ L∞) and some unbounded f ,these are bounded operators with norm ‖ · ‖t.For f, g bounded, with “sufficiently many” bounded derivatives, there are known deformationquantization conditions,

• (0) limt→0‖T (t)f ‖t = ‖f‖∞

• (1) limt→0‖T (t)f T

(t)g − T (t)

fg ‖t = 0.

We exhibit bounded real-analytic functions f, g so that (1) fails. On the positive side, forthe space VMO of functions with vanishing mean oscillation, we show that (1) holds for allf, g in the sup-norm and complex-conjugate closed algebra A = VMO ∩ L∞ and, in fact, Ais the largest such subalgebra of L∞. (1) also holds for all f, g ∈ UC (uniformly continuousfunctions, bounded or not) while (0) holds for all f ∈ L∞.

Raul CurtoUniversity of [email protected]: Toral and Spherical Aluthge TransformsAbstract: We introduce two natural notions of multivariable Aluthge transforms (toral andspherical), and study their basic properties. In the case of 2-variable weighted shifts, wefirst prove that the toral Aluthge transform does not preserve (joint) hyponormality, insharp contrast with the 1-variable case. Second, we identify a large class of 2-variableweighted shifts for which hyponormality is preserved under both transforms. Third, weconsider whether these Aluthge transforms are norm-continuous. Fourth, we study how theTaylor and Taylor essential spectra of 2-variable weighted shifts behave under the toral andspherical Aluthge transforms; as a special case, we consider the Aluthge transforms of theDrury-Arveson 2-shift. Finally, we discuss the class of spherically quasinormal 2-variableweighted shifts, which are the fixed points for the spherical Aluthge transform.

The talk is based on joint work with Jasang Yoon.

Francesco Di PlinioUniversity of [email protected]: Maximal averages and singular integrals along vector fields in higher dimension



mailto: [email protected]

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Abstract: It is a conjecture of Zygmund that the averages of a square integrable functionover line segments oriented along a Lipschitz vector field on the plane converge pointwisealmost everywhere. This statement is equivalent to the weak L2 boundedness of the direc-tional maximal operator along the vector field. A related conjecture, attributed to Stein, isthe weak L2 boundedness of the directional Hilbert transform taken along a Lipschitz vectorfield. In this talk, we will discuss recent partial progress towards Steins conjecture obtainedin collaboration with I. Parissis, and separately with S. Guo, C. Thiele and P. Zorin-Kranich.In particular, I will discuss the recently obtained sharp bound for the Hilbert transform alongfinite order lacunary sets in all dimensions, the singular integral counterpart of the Parcet-Rogers characterization of Lp boundedness for the directional maximal function in higherdimensions.

Ben DodsonJohns Hopkins [email protected]: Global well - posedness and scattering for the cubic wave equation in three dimensionsAbstract: In this talk we discuss a global well-posedness and scattering result for the cubicwave equation in three dimensions. We prove this for initial data lying in a space that iscritical under the scaling.

Dong DongUniversity of Illinois [email protected]: Hilbert transforms in a 3 by 3 matrixAbstract: We will present some variants of Hilbert transforms, with a focus on the tech-niques used in obtaining the boundedness property and the applications of these techniquesin number theory, ergodic theory, etc.

Mengxia DongUniversity of [email protected]: Existence of Extremal functions for higher order derivatives Caffarelli-Kohn-NirenberginequalitiesAbstract: Consider the higher order derivatives Caffarelli-Kohn-Nirenberg inequality(Lin,1986): (∫

RN

|Dju|r dx|x|s) 1

r ≤ C(∫

RN

|Dmu|p dx|x|µ

)ap(∫

RN

|u|q dx|x|σ

) 1−aq,

where C = C(p, q, r, µ, σ, s,m, j) and p, q, r, µ, σ, s,m, j are some parameters satisfying somebalanced conditions.I proved the existence of optimal functions in a family of the higher order derivativesCaffarelli-Kohn-Nirenberg inequality under numerous circumstances of parameters. In addi-tion to that, I study the compactness of weighted Sobolev space for higher order derivativesand established Hm,p

µ (Ω) ∩ Lqσ(Ω) → Hj,rs (Ω) is a compact embedding under some range of




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the parameters.

Lawrence FialkowSUNY New [email protected]: The core variey of a multisequence in the truncated moment problemAbstract: ”Let β ≡ β(m) be an n-dimensional multi-sequence of degree m. The TruncatedMoment Problem asks for conditions on β such that there exists a positive Borel measure µon Rn satisfying βi =

∫xidµ (|i| ≤ m). We associate to β an algebraic variety in Rn called

the core variety in such a way that β has a representing measure µ (as above) if and only ifthe core variety is nonempty.

Dawit Habte GebreUniversity of L’[email protected]: Analysis of Turbulent Hydromagnetic Flow with Radiative Heat over a Moving Ver-tical Plate in a Rotating SystemAbstract: In this paper, the combined effects of magnetic fields, buoyancy force, thermalradiation, viscous and Ohmic heating on turbulent hydromagnetic flow of an incompressibleelectrically conducting fluid over a moving vertical plate in a rotating system is investigatednumerically. The governing equations are reduced to non-linear ordinary differential equa-tions using the time-averaged approach known as Reynolds-averaged NavierStokes equations(or RANS equations) and tackled by employing an efficient Runge-Kutta Fehlberg integra-tion technique coupled with shooting scheme. Graphical results showing the effects of variousthermophysical parameters on the velocity, temperature, local skin friction and local Nusseltnumber are presented and discussed quantitatively.

Roozbeh GharakhlooIndiana University-Purdue University [email protected]: On the asymptotics of Toeplitz+Hankel determinantsAbstract: We want to analyse the asymptotics of a Toeplitz+Hankel determinant withToeplitz symbol φ(z) and Hankel symbol w(z). When symbols φ(z) and w(z) are related inspecific ways, the asymptotics of T+H determinants have been studied by E. Basor and T.Ehrhardt and by P. Deift, A. Its and I. Krasovsky. The distinguishing feature of this work isthat we do not assume any relations between the sympbols φ(z) and w(z). We approach thisproblem by analysing a 4 by 4 Riemann Hilbert problem. In this talk I will introduce theclass(es) of symbols for which we have been able to analyse the Riemann-Hilbert problem.This work is part of the joint research project with Alexander Its, Percy Deift and IgorKrasovsky.

Guihua GongUniversity of Puerto Rico




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[email protected]: On the classification of unital simple separable nuclear C∗ algebrasAbstract: C∗ algebras, as noncommutative spaces, have significant applications in the studyof differential geometry, topology of manifold and dynamical systems. Simple C∗ algebrascan be regarded as noncommutative single point spaces, which are basic building blocks inthe theory of C∗ algebras. Recent year, there are several important breakthroughs in theElliott program of classification of simple nuclear C* algebras. In this talk, I will presentthe complete classification of unital simple separable C∗ algebras of finite nuclear dimensiondue to Kirchberg-Phillips, Gong-Lin-Niu, Elliott-Gong-Lin-Niu, and Tikusis-White-Winter.

Walton GreenClemson [email protected]: Harmonic Analysis Proof of the Boundary Observability for the Wave EquationAbstract: We give a harmonic analysis proof of the Neumann boundary observability inequal-ity for the wave equation in arbitrary space dimension. The advantages of this approach arethe simplicity of the constant as well as the elementary nature of the entire proof.

Raffael HaggerLeibniz University [email protected]: Compactness and Essential Spectra on Bounded Symmetric DomainsAbstract: Characterizing all the compact operators on particular Banach or Hilbert spaces isa non-trivial problem that always attracted a lot of interest. In particular, if we want to ap-proach a fruitful Fredholm theory, we need to understand the compact operators. In this talkwe want to characterize the compact operators acting on the Bergman space over boundedsymmetric domains and study the implications for the essential spectrum of Toeplitz oper-ators.

Hyun Kyoung KwonUniversity of [email protected]: On the similarity of Cowen-Douglas operatorsAbstract: We consider some recent progress on the similarity characterization of Cowen-Douglas operators using the associated eigenvector bundles.

Jungang LiUniversity of [email protected]: Concentration-compactness principles on the Heisenberg group and Riemannian man-ifolds






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Abstract: Concentration-compactness principle plays an important role in geometric analysisand PDEs. All the existing proofs of the concentration-compactness principles for Trudinger-Moser inequalities even in the Euclidean spaces in the literature have to use the Polya-Szegoinequality of symmetrization. We will give proofs of such principle in settings such as theHeisenberg group and Riemannian manifolds where such Polya-Szego inequality does nothold. Applications to nonlinear PDEs are given. These are joint works with Guozhen Lu(UConn) and Maochun Zhu (Jiangsu University).

Cezar LupuUniversity of [email protected]: Analytic aspects in the evaluation of multiple zeta values and multiple Hurwitz zetavaluesAbstract: In this talk, we shall discuss about some new results in the evaluation of some mul-tiple zeta values (MZV). After a careful introduction of the multiple zeta values (Euler-Zagiersums) we point out some conjectures back in the early days of MZV and their combinatorialaspects.At the core of our talk, we focus on Zagier’s formula for the multiple zeta values, ζ(2, 2, . . . , 2, 3, 2, 2, . . . , 2)and its connections to Brown’s proofs of the conjecture on the Hoffman basis and the zig-zagconjecture of Broadhurst in quantum field theory. Zagier’s formula is a remarkable exampleof both strength and the limits of the motivic formalism used by Brown in proving Hoffman’sconjecture where the motivic argument does not give us a precise value for the special multi-ple zeta values ζ(2, 2, . . . , 2, 3, 2, 2, . . . , 2) as rational linear combinations of products ζ(m)π2n

with m odd. The formula is proven indirectly by computing the generating functions of bothsides in closed form and then showing that both are entire functions of exponential growthand that they agree at sufficiently many points to force their equality.By using the Taylor series of integer powers of arcsin function and a related result aboutexpressing rational zeta series involving ζ(2n) as a finite sum of Q-linear combinations of oddzeta values and powers of π, we derive a new and direct proof of Zagier’s formula in the spe-cial case ζ(2, 2, . . . , 2, 3). Towards the end of the talk, we present a more general formula forζ(2, 2, . . . , 2,m), with m ≥ 3 integer. We also discuss similar results for the multiple t-values.

Pan MaCentral South University (China)[email protected]: Compactness of Toeplitz operators and Hankel operators on model spacesAbstract: We characterized the compactness of Toeplitz operators and Hankel operators onmodel spaces with bounded symbol vis product of Hankel operators on Hardy space andfunction algebras.

Javad MashreghiLaval [email protected]




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Title: Some Preserver theorems in Hp SpacesAbstract: We generalize the Gleason - Kahane - Zelazko theorem to modules. As an ap-plication, we show that every linear functional on a Hardy space that is non-zero on outerfunctions is a multiple of a point evaluation. A further consequence is that every line arendomorphism of a Hardy space that maps outer functions to nowhere-zero functions is aweighted composition operator. In neither case is continuity assumed.

Azita MayeliQueens Community College and The Graduate Center, City University of New [email protected]: Orthogonal Gabor bases on finite vector spacesAbstract: We study orthogonal Gabor bases on the d-dimensional vector spaces of finitedimensions over the cyclic groups of prime order. The investigation has analytic, numbertheoretic and combinatorial aspects. The analytic arguments comes in the form of Fourieranalytic inequalities, the number theoretic aspects involve the analysis of exponential sumsand the combinatorial arguments involve tiling and the study of direction sets.

Kathryn McCormickUniversity of [email protected]: Riemann surfaces, holomorphic bundles, and boundary representationsAbstract: This talk presents an analysis of a class of operator algebras constructed as cross-sectional algebras of certain holomorphic matrix bundles, partly inspired by the bundle shiftsof Abrahamse and Douglas (1976). The objective is to understand the boundary represen-tations of the containing C∗-algebra, i.e. the noncommutative Choquet boundary for eachof our operator algebras. More specifically, let R be a finitely connected, bordered Riemannsurface with fundamental group G, where we view G as acting on the unit disk, D. Then

the action of G on D extends to a free and proper action of G on a certain open subset Dof D which has quotient space R; i.e., D/G ' R. Using a representation ρ of G in PUn(C),one builds a flat Mn(C)-bundle E(R, ρ) over R in the standard manner. The operator alge-bra in question, denoted Γh(R,E(R, ρ)), is the collection of all continuous cross sections ofE(R, ρ) that are holomorphic on R. The algebra Γh(R,E(R), ρ)) generates the C∗-algebra ofall continuous cross sections of E(R, ρ), written Γc(R,E(R, ρ)). The boundary representa-tions of Γc(R,E(R, ρ)) for Γh(R,E(R, ρ)) are calculated, and shown that they correspond toevaluations on the boundary of R. While the result is perhaps expected, the proof requiresseveral theorems of Arveson addressing the noncommutative setting.

Arthur ParzygnatUniversity of [email protected]: Categories in Probability




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Abstract: Motivated by the commutative Gelfand-Naimark theorem that provides a naturalequivalence between continuous maps on compact Hausdorff spaces and C∗-algebra homo-morphisms of commutative C∗-algebras, we construct a category of stochastic maps on suchspaces and describe the functorial duality between these maps and positive unital maps ofcommutative C∗-algebras.

Bhupendra PaudyalCentral State [email protected]: The lattices of invariant subspaces of a class of operators on the Hardy spaceAbstract: This work describes the lattice of invariant subspaces of the shift plus a positiveinteger multiple of the complex Volterra operator on the Hardy space. Our work was moti-vated by a paper by Ong who studied the real version of the same operator.

Stefanie PetermichlUniversity of [email protected]: On the matrix A2 conjectureAbstract: The condition on the matrix weight W that is necessary and sufficient for theboundedness of the Hilbert transform acting on vector functions in the matrix weighted L2

space, the matrix A2 condition, is known since 1997 (Treil-Volberg). One motivation forthis question stems from the understanding of past and future in multi-variate stationarystochastic processes. Good or sharp quantitative norm control depending on the A2 char-acteristic of the weight in the ’scalar’ case dates to 2007 (P.). Despite notable improvementsince then and many new techniques that apply in the scalar setting, the matrix A2 questionfor the Hilbert transform remains unsolved. We present the best to date estimate (Nazarov-P.-Treil-Volberg), via the use of certain convex bodies and a domination principle in the area.We also present the first sharp estimate of a singular operator in this setting, the matrixweighted square function (Hytonen-P.-Volberg).

Gabriel PrajituraUniversity of Brockport, [email protected]: Linear ChaosAbstract: We will discuss how various concepts of chaos translate in terms of bounded linearoperators on Hilbert spaces and what relations are between them.

Mihai PutinarUC Santa [email protected]: Positivity transformers





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Abstract: The question what operations on the distance function of a metric space turn thelatter into an isometric subset of a Hilbert space prompted around 1930s a thorough studyof distance geometry with positive matrices techniques.Out of this context Schoenberg, von Neumann and Loewner produced fundamental results.The next generation of harmonic analysts extended the same circle of ideas to homogeneousspaces. The interplay between function theory (Laplace transform methods and interpolationof series of exponentials) with purely matrix analysis tools was prevalent in the area duringmany decades. Very recently, statisticians found useful these partially forgotten gems oflast century analysis, in their attempt to condition and analyze correlation matrices of largesystems of random variables.The talk will be focused on the main historical moments of matrix positivity preservers andwill touch some recent progress made possible thanks to symmetric function theory.Based on joint work with Alex Belton, Dominique Guillot and Apoorva Khare.

Anca RadulescuState University of New York at New [email protected]: Template iterations of quadratic maps and hybrid Mandelbrot setsAbstract: We consider iterations of two quadratic maps fc0 = z2 + c0 and fc1 = z2 + c1,according to a prescribed binary sequence, which we call template. We study the asymp-totic behavior of the critical orbit, and define the Mandelbrot set in this case as the locusfor which this orbit is bounded. However, unlike in the case of single maps, this concept canbe understood in several ways. For a fixed template, one may consider this locus as a subsetof the parameter space in (c0, c1) ∈ C2; for fixed quadratic parameters, one may considerthe set of templates which produce a bounded critical orbit. In this paper, we consider bothsituations, as well as hybrid combinations of them, we study basic topological properties ofthese sets and propose applications.

Pablo Jimenez-RodriguezKent State [email protected]: On some trivial (and not so trivial) inequalities for convex functions.Abstract: We present an inequality that real convex functions fulfill and study what impli-cations this inequality may provide. We will focus specially in the implications inside of thetrend of lineability and spaceability of sets.

Benjamin RussoUniversity of [email protected]: A Generalization of the Fock SpaceAbstract: In this talk we will introduce a generalized Fock space which uses the Mittag-Leffler function as its reproducing kernel. This space has been featured in the developmentof a finite difference method. However, it has yet to be investigated as a space of entire




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functions. We will discuss some preliminary results in comparison to the Fock space andpotential applications. This is joint work with Joel Rosenfeld and Warren Dixon.

Lev [email protected]: The generelized scattering problems, ergodic type theorems.Abstract: We prove that for the Schredinger radial equation with Coulomb type poten-tial the generalized dynamical scattering operator coincides with the generalized stationaryscattering operator. The same result is proved for the Dirac radial equation. So, we obtainquantum mechanical analogue of ergodic results in the classical mechanics.

Meredith SargentWashingtong University St. [email protected]: Carlson’s Theorem for Different MeasuresAbstract: We use an observation of Bohr connecting Dirichlet series in the right half planeC+ to interpret Carlson’s theorem about integrals in the mean as a special case of the ergodictheorem by considering any vertical line in the half plane as an ergodic flow on the polytorus.Of particular interest is the imaginary axis because Carlson’s theorem for Lebesgue measuredoes not hold there. In this note, we construct measures for which Carlson’s theorem doeshold on the imaginary axis for functions in the Dirichlet series analog of the disk algebraA(C+).

Eric [email protected]: A two weight local Tb theorem for the Hilbert transformAbstract: We prove that the Hilbert transform is bounded from one weighted L2 space toanother if and only if the A2 and energy conditions hold, as well as testing conditions takenover weakly accretive families with Lp integrability, p > 2. This is joint work with Chun-YenShen and Ignacio Uriarte-Tuero.

Wilhelm [email protected]: Structure theorems for intertwining wave operators in three dimensionsAbstract: In the 1990s Kenji Yajima carried out a comprehensive analysis of the Lp bound-edness of the classical wave operators from scattering theory. In recent joint work withMarius Beceanu, we obtained a representation of the wave operators in R3 as a superpo-sition of translations and reflections. This work combines elements of Yajima’s work withmethods from harmonic analysis. Specifically, we rely on both Stein-Tomas restriction the-ory of the Fourier transform, and Wiener’s theorem on inversion in a convolution algebra,albeit a complicated one. The latter is essentially a summation method and is used to suma Born series with large terms. The necessary condition for invertibility needed in Wienerinversion comes from spectral theory developed about 13 years ago. In effect, this amounts





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to the classical Agmon-Kato-Kuroda theory but completely redone by means of Stein-Tomastype results.

Petr SieglUniversity of [email protected]: Non-accretive Schrodinger operators and exponential decay of their eigenfunctionsAbstract: We consider non-self-adjoint electromagnetic Schrodinger operators on arbitraryopen sets with complex scalar potentials whose real part is not necessarily bounded frombelow. Under a suitable sufficient condition on the potentials, we introduce a Dirichletrealization as a closed densely defined operator with non-empty resolvent set and show thatthe eigenfunctions corresponding to discrete eigenvalues satisfy an Agmon-type exponentialdecay. Remarks on the spectral convergence of domain truncations and completeness ofeigenfunctions will be given.The talk is based on: [1] D. Krejcirık, N. Raymond, J. Royer and P. Siegl: Non-accretiveSchrodinger operators and exponential decay of their eigenfunctions, Israel Journal of Math-ematics, to appear, arXiv:1605.02437.[2] S. Bgli, P. Siegl, and C. Tretter: Approximations of spectra of Schrodinger operatorswith complex potentials on Rd, Communications in Partial Differential Equations 42, (2017),1001-1041, arXiv:1512.01826

Mihai StoiciuWilliams [email protected]: Bounds for the Pseudospectra of Various Classes of Matrices and OperatorsAbstract: We investigate the ε-pseudospectra of various classes of non-normal matrices andoperators. In particular, we are interested in the shape of the pseudospectrum, regardedas a subset of the complex plane. We provide explicit lower and upper bounds for the ε-pseudospectra of bi-diagonal and tri-diagonal matrices and operators.

Qijun TanPenn State [email protected]: Asymptotic containment of representations and the spherical Plancherel formualAbstract: We will introduce the notion of asymptotic contianment of representations ofC∗ algebras, which is a generalization of weak containment of representations. The newdefinition enables us among other things to compute the spectral measure of a difficult rep-resentation from an easy one. We will show how to apply this to prove Harish-Chandra’sspherical Plancherel formula. This is a joint work with Nigel Higson.

Andrei TarfuleaUniversity of [email protected]





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Title: Improved Estimates for Thermal Fluid EquationsAbstract: We consider two hydrodynamic model problems (one incompressible and one com-pressible) with three dimensional fluid flow on the torus and temperature-dependent viscosityand conductivity. The ambient heat for the fluid is transported by the flow and fed by thelocal energy dissipation, modeling the transfer of kinetic energy into thermal energy throughfluid friction. Both the viscosity and conductivity grow with the local temperature. Weprove a strong a priori bound on the enstrophy of the velocity weighed against the tempera-ture for initial data of arbitrary size, requiring only that the conductivity be proportionatelylarger than the viscosity (and, in the incompressible case, a bound on the temperature as aMuckenhoupt weight).

Daniel [email protected] BerkeleyTitle: Energy-critical Yang-MillsAbstract: The hyperbolic Yang-Mills equation is one of the fundamental geometric nonlinearwave equations. The aim of this talk will be to provide an overview of the recent work, jointwith Sung-Jin Oh, whose aim is to provide a proof of the Threshold Conjecture for Yang-Mills. This asserts that global well-posedness and scattering holds for all solutions below theground state energy.

Razvan TeodorescuUniversity of South [email protected]: Stochastic regularization of singularities in free boundary problemsAbstract: We discuss an unexpected link between the Lax-Levermore weak continuation ofsolutions to hyperbolic PDEs past a cusp singularity and free stochastic processes.

Ebru ToprakUniversity of Illinois [email protected]: Dispersive Estimates For Massive Dirac OperatorsAbstract:I will present a study on the L1 → L∞ dispersive estimates for the two and threedimensional massive Dirac equation with a potential. In two dimension, we show that thet−1 decay rate holds if the threshold energies are regular or if there are s-wave resonances atthe threshold. We further show that, if the threshold energies are regular then a faster decayrate of t−1(log t)−2 is attained for large t, at the cost of logarithmic spatial weights, whichis not the case for the free Dirac equation. In three dimension, we show that the solutionoperator is composed of a finite rank operator that decays at the rate t−1/2 plus a term thatdecays at the rate t−3/2.

Sergei TreilBrown University




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[email protected]: Finite rank perturbations, Clark model, and matrix weightsAbstract: For a unitary operator U all its contractive perturbations U + K, ‖U + K‖ ≤ 1by finite rank operators K with a fixed range R, RanK ⊂ R can be parametrized by

TΓ

:= U +B(Γ− ICd

)B∗U, Γ : Cd → Cd, ‖Γ‖ ≤ 1,

where B is a fixed unitary operator B : Cd → R.Under the natural assumptions that R is a ∗-cyclic subspace for U and Γ is a strict con-traction, the operator T

Γis the so-called completely non-unitary (c.n.u) contraction, so it is

unitarily equivalent to its Sz.-Nagy–Foias functional model.The Clark operator is a unitary operator that intertwines the operator T

Γ(which we assume

is given to us in the spectral representation of the operator U) and its functional model.Description of such operator is the subject of Clark theory.I will completely describe the Clark operator in its adjoint for the general finite rank per-turbations. The adjoint Clark operator is given by the vector-valued Cauchy transform, andthe direct Clark operator is given by simple algebraic formulas involving boundary valuesof functions from the model space. Weighted estimates with matrix valued weights appearnaturally in this context.The case of rank one perturbation of a unitary operator with purely singular spectrum wascompletely described (from a different point of view) by D. Clark, and later further developedby A.Aleksandrov and then by A. Poltoratski; the case of general rank one perturbations wasresolved by Liaw–Treil. In the case of perturbations of rank d > 1, some new phenomenarequiring careful investigation appear, and are resolved.The talk is based on a joint work with C. Liaw.

Gennady UraltsevCornell [email protected]: Uniform Bounds for the Bilinear Hilbert TransformAbstract: We will talk about uniform bounds for the Bilinear Hilbert Transform in the fullBanach range of expected exponents. The dyadic analog of this problem has been solvedby Oberlin and Thiele (2010). We use the framework embedding maps into the time-scale-frequency space and outer measure Lp space theory and its iterated generalization to avoidthe necessity for tree projections that represented a major obstruction for uniform bounds.

Monica [email protected]: Almost sure scattering for the cubic NLS in four dimensionsAbstract: I will discuss recent work with R. Killip and J. Murphy on almost sure scatteringfor the energy-critical NLS in four space dimensions with radial randomized initial data.

Zhenfu Wang




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University of [email protected]: Quantitative estimates of propagation of chaos for stochastic systems with W−1,∞

kernelAbstract: We derive quantitative estimates proving the propagation of chaos for large sto-chastic systems of interacting particles. We obtain explicit bounds on the relative entropybetween the joint law of the particles and the tensorized law at the limit. We have to developfor this new laws of large numbers at the exponential scale. But our result only requires veryweak regularity on the interaction kernel in the negative Sobolev space W−1,∞, thus includingthe Biot-Savart law and the point vortices dynamics for the 2d incompressible Navier-Stokes.

Hugo J. WoerdemanDrexel [email protected]: Complete spectral sets and numerical rangeAbstract: We define the complete numerical radius norm for homomorphisms from any op-erator algebra into B(H), and show that this norm can be computed explicitly in terms ofthe completely bounded norm. This is used to show that if K is a complete C-spectral setfor an operator T , then it is a complete M -numerical radius set, where M = 1

2(C + C−1).

In particular, in view of Crouzeix’s theorem, there is a universal constant M (less than 5.6)so that if P is a matrix polynomial and T ∈ B(H), then w(P (T )) ≤ M‖P‖W (T ). When

W (T ) = D, we have M = 54.

Jianchao WuPenn State [email protected]: Noncommutative dimensions and crossed product C∗-algebrasAbstract: C*-algebras are a kind of operator algebras that are tailored to describe non-commutative (i.e., quantum) topological spaces through analytical means. A major andinexhaustible source of C*-algebras lies in the construction of crossed products from topo-logical dynamical systems, which has occupied a central position throughout the history ofC*-algebra theory. On the other hand, the dimension theory of C*-algebras, which studiesanalogs of classical dimensions for topological spaces, is young but has been gaining mo-mentum lately thanks to the pivotal role played by the notion of finite nuclear dimensionin the classification program of simple separable nuclear C*-algebras. The convergence ofthese two topics leads to the question: When does a crossed product C*-algebra have finitenuclear dimension? I will present some recent work on this problem.

Yunyun [email protected] of West Virginia, Institute of TechnologyTitle: Some subtleties in the relationships among heat kernel invariants, eigenvalue distri-butions, and quantum vacuum energy





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Abstract: A common tool in Casimir physics (and many other areas) is the asymptotic(high-frequency) expansion of eigenvalue densities, employed as either input or output ofcalculations of the asymptotic behavior of various Green functions. Here we show how re-cent observations of Kolomeisky et al. [Phys. Rev. A 87 (2013) 042519] fit into the establishedframework of the distributional asymptotics of spectral functions.

Xueying YuUniversity of [email protected]: Global well-posedness and scattering for the quintic NLS in two dimensionsAbstract: We consider the Cauchy initial value problem for the defocusing quintic nonlinearSchrodinger equation in R2 with general data in the critical space H

12 (R2). We show that if

a solution remains bounded in H12 (R2) in its maximal interval of existence, then the interval

is infinite and the solution scatters.

A. Shadi Tahvildar-ZadehRutgers [email protected]: General Relativity at the Atomic ScaleAbstract: In this talk I will describe how our knowledge of general relativity can help usgain new insight into the microscopic world of elementary particles and their quantum lawsof motion.

Ruhan ZhaoUniversity at Brockport, State University of New [email protected]: On Berezin type operators and Toeplitz operatorsAbstract: In this talk we introduce a type of integral operators associated with a posi-tive measure and resembling the Berezin transforms on the unit ball. Boundedness andcompactness of these Berezin type operators between weighted Bergman spaces are charac-terized using Carleson measures. It has been found that the results are closely relative tothose of Toeplitz operators between weighted Bergman spaces. This is a joint work withGabriel Prajitura and Lifang Zhou.




NEAM 2 - University at Albany, SUNYmb533919/NEAM 2017 abstracts.pdf · 2017-10-13 · NEAM 2...

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