The Department of Mathematics is pleased to host a variety of events throughout the year. For additional information about our seminars, lectures, colloquia, and related activities, please call (716) 645-6284 or contact us via general inquiry email: mathematics@buffalo.edu

Thank you for your interest in our events.

*Join us for upcoming seminars and special events:*

Algebra Seminar**Adam Sikora, University at Buffalo**

Stated skein algebras and a geometric approach to quantum groups

4:00PM, Mathematics Building room 250

Analysis Seminar**Joseph Leung, Rutgers University**

Second moment for GL(3) L-functions in the critical line

4:00PM, 250 Math Building

Applied Math Seminar**Nicholas Ossi, UB**

Time-periodic breather solutions of the discrete defocusing Ablowitz-Ladik equation with large background amplitude.

3:00PM, Math 250

Applied Math Seminar**Katerina Gkogkou, Tulane University**

TBA.

3:00PM, Math 250

Geometry and Topology Seminar**Robbie Lyman (Rutgers University)**

TBA

4:00PM, 122 Mathematics Building

Analysis Seminar**Guo Chuan Thiang, Peking University**

4:00PM, 250 Math Building

Geometry and Topology Seminar**Katherine Goldman (Ohio State University)**

CAT(0) and cubulated Shepherd groups

4:00PM, 122 Mathematics Building

Algebra Seminar**Artan Sheshmani, Harvard/BIMSA**

4:00PM, Zoom (please email achirvas@buffalo.edu)

Geometry and Topology Seminar**Tam Cheetam-West (Yale)**

Profinite rigidity of some fibered, hyperbolic 3-manifold groups

4:00PM, 122 Mathematics Building

Applied Math Seminar**Zechuan Zhang, UB**

Inverse spectral theory for the periodic self-adjoint Zakharov-Shabat and IST for the defocusing NLS equation with periodic BCs.

3:00PM, Math 122

Algebra Seminar**David Hernandez, Université Paris Cité**

A new Weyl group action and a cluster structure for representations of shifted quantum groups

4:00PM, Zoom (please email achirvas@buffalo.edu)

Analysis Seminar**Jintao Deng, SUNY at Buffalo**

The maximal rational Novikov conjecture and the coarse embeddability

4:00PM, 250 Math Building

Geometry and Topology Seminar**Luya Wang (Stanford)**

Deformation inequivalent symplectic structures and Donaldson's four-six question

4:00PM, via Zoom

Algebra Seminar**Peter Koroteev, UB**

The Diamond of Integrability

4:00PM, : Zoom (please email achirvas@buffalo.edu)

Analysis Seminar**Jingbo Xia, SUNY at Buffalo**

Fock space: a bridge between Fredholm index and the quantum Hall effect

4:00PM, 250 Math Building

Analysis Seminar**Mohan Ramachandran, SUNY at Buffalo**

Maximal Spectrum, Stone Cech, and Stone Weierstrass theorems

4:00PM, 250 Math Building

Algebra Seminar**Minh-Tam Quang Trinh, MIT**

Hecke Traces, Braid Varieties, and Springer Actions

4:00PM, 250 Mathematics Building

Geometry and Topology Seminar**Marie Trin (Institut Mathématiques de Rennes)**

Counting* *arcs of the same type

4:00PM, 122 Mathematics Building

Analysis Seminar**Jintao Deng, SUNY at Buffalo**

The maximal rational Novikov conjecture and the coarse embeddability, Part II

4:00PM, 250 Math Building

Special Event**Jintao Deng, SUNY at Buffalo**

The maximal rational Novikov conjecture and the coarse embeddability, Part II

4:00PM, 250 Math Building

Applied Math Seminar**Esteban Vargas Bernal, Arizona State University**

InfoMap for absorbing random walks.

3:00PM, Math 122

Algebra Seminar**Chengze Duan, University of Maryland**

College Park

Good-position braids, transversal slices andaffine Springer fibers

4:00PM, Zoom (please email achirvas@buffalo.edu)

Applied Math Seminar**Anastassiya Semenova, University of Washington**

Water Waves from Stokes to Now.

3:00PM, Math 250

Geometry and Topology Seminar**Johanna Mangahas (UB)**

(Non-)Recognizing Spaces for Stable Subgroups

4:00PM, 122 Mathematics Building

Algebra Seminar**Samuel DeHority, Columbia**

Flat connections and toroidal algebras

4:00PM, Zoom (please email achirvas@buffalo.edu)

Geometry and Topology Seminar**Carolyn Abbott (Brandeis University)**

Morse boundaries of CAT(0) cubical groups

4:00PM, 122 Mathematics Building

Analysis Seminar**Liang Guo, East China Normal University**

Hilbert-Hadamard spaces and the equivariant coarse Novikov conjecture

4:00PM, 250 Math Building

Algebra Seminar**Joe Kramer-Miller, Lehigh University**

Transcendental properties of the Artin-Hasse exponential modulo p

3:00PM, 250 Mathematics Building

Analysis Seminar**Wencai Liu, Texas A&M University**

Algebraic geometry, complex analysis and combinatorics in spectral theory of periodic graph operators

4:00PM, 250 Math Building

Colloquium**Indira Chatterji (University of Côte d'Azur / Fields Institute)**

Groups and geometry

4:00PM, 250 Mathematics Building

Applied Math Seminar**Alexandr Chernyavskiy, UB**

Dark-bright soliton perturbation theory for the Manakov system.

3:00PM, Math 122

Geometry and Topology Seminar**Indira Chatterji (University of Côte d'Azur / Fields Institute)**

Property T versus aTmenability

Abstract : A group has property T if any action on a Hilbert space has a fixed point, and a group is called aTmenable if it admits a proper action on a Hilbert space by affine isometries. I will review what classical groups have property T, or aTmenability, or neither, how those notions appeared and what they are good for.

4:00PM, 122 Mathematics Building

Algebra Seminar**Dani Szpruch, Open University of Israel**

An analog of the Hasse-Davenport product relation for \(\epsilon\)-factors and an application

3:00PM, 250 Mathematics Building

Analysis Seminar**Andy Zucker, University of Waterloo**

Ultracoproducts and weak containment for flows of topological groups

4:00PM, 250 Math Building

Applied Math Seminar**Anna Vainchtein, University of Pittsburgh**

Supersonic fronts and pulses in a lattice with hardening-softening interactions.

3:00PM, Math 122

Algebra Seminar**Thomas Creutzig, Edmonton/Erlangen**

Representation theory of affine VOAs

4:00PM, Zoom (please email achirvas@buffalo.edu)

I will give an overview on the state of the art in this area.

Colloquium**Tomasz Mrowka, MIT**

2023-24 Myhill Lecture #1

4:00PM

Colloquium**Tomasz Mrowka, MIT**

2023-24 Myhill Lecture #2

4:00PM

Colloquium**Tomasz Mrowka, MIT**

2023-24 Myhill Lecture #3

4:00PM

Algebra Seminar**Vasily Krylov, MIT**

Around the Hikita-Nakajima conjecture

4:00PM, Zoom (please email achirvas@buffalo.edu

Analysis Seminar**Xin Ma, Fields Institute**

Soficity, Amenability, and LEF-ness for topological full groups

4:00PM, 250 Math Building

Colloquium**Dr Willy Hereman, Colorado School of Mines**

** **Symbolic** **computation of solitary wavesolutions and solitons through homogenization of degree

4:00PM, Mathematics Building room 250

A simplified version of Hirota's method for thecomputation of solitary waves and solitons of nonlinear PDEs will be presented.The approach requires a change of dependent variable so that the transformedPDE is homogenous of degree in the new variable.

The resulting homogenous PDE does not have tobe quadratic and the method still applies if its bilinear form is not known.Solitons are then computed using a perturbation scheme involving linear andnonlinear operators. For soliton equations the scheme terminates after a finitenumber of steps. To illustrate the approach, solitons are computed for a classof fifth-order KdV equations due to Lax, Sawada-Kotera, and Kaup-Kupershmidt.

Homogenization of degree also allows one tofind solitary wave solutions of nonlinear PDEs that are not completelyintegrable. Examples include the Fisher and FitzHugh-Nagumo equations, and acombined KdV-Burgers equation. When applied to a wave equation with a cubicsource term, the method leads to a `bi-soliton' solution which describes thecoalescence of two wavefronts.

The method is largely algorithmic andimplemented in Mathematica. A demonstration of the software packagePDESolitonsSolutions will be given.

Applied Math Seminar**Willy Hereman, Colorado School of Mines**

Symbolic computation of conservation laws of nonlinear partial differential equations.

3:00PM, Math 250

Algebra Seminar**Ivan Loseu, Yale**

Harish-Chandra centers for affine Kac-Moody algebras in positive characteristic Abstract : This talk is based on a joint work in progress with Gurbir Dhillon. A remarkable theorem of Feigin and E. Frenkel from the early 90s describes the center of the universal enveloping algebra of an(untwisted) affine Kac-Moody Lie algebra at the so-called critical level proving a conjecture of Drinfeld: the center in question is the algebra of polynomial functions on an infinite-dimensional affine space known as the space of opers. In our work we study a part of the center in positive characteristic \(p\) at an arbitrary non-critical level. Namely, we prove that the algebra of loop-group invariants in the completed universal enveloping algebra is still the algebra of polynomials on an infinite-dimensional affine space that is ``\(p\) times smaller than the Feigin-Frenkel center''. In my talk I will introduce all necessary notions, state the result, explain motivations and examples.

4:00PM, Zoom (please email achirvas@buffalo.edu)

Title: Harish-Chandra centers for affine Kac-Moody algebras in positive characteristic

Abstract : This talk is based on a joint work in progress with Gurbir Dhillon. A remarkable theorem of Feigin and E. Frenkel from the early 90s describes the center of the universal enveloping algebra of an(untwisted) affine Kac-Moody Lie algebra at the so-called critical level proving a conjecture of Drinfeld: the center in question is the algebra of polynomial functions on an infinite-dimensional affine space known as the space of opers. In our work we study a part of the center in positive characteristic \(p\) at an arbitrary non-critical level. Namely, we prove that the algebra of loop-group invariants in the completed universal enveloping algebra is still the algebra of polynomials on an infinite-dimensional affine space that is ``\(p\) times smaller than the Feigin-Frenkel center''. In my talk I will introduce all necessary notions, state the result, explain motivations and examples.

Applied Math Seminar**Stephen Anco, Brock University**

Integrable multi-component nonlinear evolution equations and their bi-Hamiltonian

structure in the AKNS formalism.

3:00PM, Math 250 - note the room change

Algebra Seminar**Professor Jie Du, University of New South Wales**

Canonical bases for quantum gl_{m|n}

4:00PM, Mathematics Building room 250

Geometry and Topology Seminar**G&T Seminar**

4:00PM, 122 Mathematics Building

Geometry and Topology Seminar**Tomasz Maszczyk (University of Warsaw)**

Foliations with rigid Godbillon-Vey class

4:00PM, 122 Mathematics Building

Algebra Seminar**Tomasz Maszczyk, University of Warsaw**

Hochschild cohomology for abstract convexity and Shannon entropy

4:00PM, 250 Math building

Analysis Seminar**Janusz Wysoczanski, University of Wroclaw**

Finitely Generated Weakly Monotone C*-algebras

4:00PM, 250 Math Building

Algebra Seminar**Anna Wysoczańska-Kula, Uniwersytet Wrocławski**

Free resolution of universal unitary quantum groups

4:00PM, 250 Mathematics Building

Analysis Seminar**Wenbo Sun, Virginia Tech**

Geometry Ramsey Conjecture over finite fields

4:00PM, 250 Math Building

Geometry and Topology Seminar**Matthew Stoffregen (Michigan State University)**

Pin(2) Floer homology and the Rokhlin invariant

4:00PM, 122 Mathematics Building

Algebra Seminar**Janusz Wysoczański, University of Wroclaw**

Hecke algebras on homogeneous trees and relationswith Hankel and Toeplitz matrices

4:00PM, 250 Mathematics Building

The Hecke algebra on homogeneous tree is a commutative algebra, spanned by particular kernels, defined on pairs of vertices \((x,y)\)and indexed by non-negative integers \(f_n(x,y)\). Each of these kernels depends on the distance between the vertices and vanishes if the distance is not equal to their index, otherwise it equals 1. We will show that the Hecke algebra is generated by \(f_1\), which satisfies quadratic (Hecke) equation. Our main interest is in showing that the Hecke algebra is MASA (i.e. Maximal Abelian SubAlgebra) in some bigger algebra.

If \(q>1\) then a geometric trick of a Y-turn on the tree will do the job. If \(q=1\), which corresponds to the tree of integers, the Y-turn is not possible, and we introduce some additional (Banach space)structure and show that the Hecke algebra is not MASA, but its commutant decomposes as a direct sum of Hankel and Toeplitz (double-infinite) matrices.

Analysis Seminar**Jakob Streipel, SUNY at Buffalo**

Stechkin's trick

4:00PM, 250 Math Building

Applied Math Seminar**Mohammad-Ali Miri, Queens College CUNY**

Analog Optical Computing: Combinatorial Optimization and Learning Unitary Operations.

3:00PM, Math 250

Algebra Seminar**Vasudevan Srinivas, UB**

Two results on \'etale fundamental groups in characteristic p

4:00PM, Mathematics Building room 250

Analysis Seminar**Jingbo Xia, SUNY at Buffalo**

The Helton-Howe trace formula for the Drury-Arveson space

4:00PM, 250 Math Building

Applied Math Seminar**Jia Zhao, Binghamton University**

General Numerical Framework for Structure-Preserving Reduced Order Models of Thermodynamically Consistent Reversible-Irreversible PDEs

3:00PM, Math 250

Geometry and Topology Seminar**Christopher Karpinski (McGill University)**

A weak Tits alternative for groups acting on buildings.

4:00PM, 122 Mathematics Building

Analysis Seminar**Raphael Ponge, Sichuan University**

Noncommutative Geometry, Semiclassical Analysis, and Weak Schatten Classes

4:00PM, 250 Math Building

Applied Math Seminar**Deniz Bilman, University of Cincinnati**

General rogue waves of infinite order: exact properties, asymptotic behaviour, and effective numerical computation.

3:00PM, Math 250

Applied Math Seminar**Tharusha Bandara, UB**

Mathematical Model on HIV and Nutrition

3:00PM, Math 250

Applied Math Seminar**Chun Liu, Illinois Institute of Technology**

Active Fluids and Applications.

3:00PM, Math 250

Hosted by UB Math on behalf of the American Mathematical Society (AMS)

Geometry and Topology Seminar**Morgan Weiler (Cornell University)**

ECH cobordism maps and infinite staircases of 4D symplectic embeddings

4:00PM, 122 Mathematics Building

Applied Math Seminar**Jiyoung Kang, Pukyong National University**

Brain Dynamics and its Control: Computational Approaches

2:00PM, Math 250 and on Zoom - contact mbichuch@buffalo.edu for link

Algebra Seminar**Yiqiang Li, University at Buffalo**

Quantum groups and edge contraction

4:00PM, 250 Math Bldg

Special Event**Solitons and the inverse scattering transform: an overview**

Solitons and the inverse scattering transform: an overview.** Abstract: **An exciting and extremely active area of research investigation is the study of solitons and the nonlinear partial differential equations that describe them. In this talk, we will discuss what solitons are, and what makes them so special. We will see when the first solitons were observed, and when the first math that describe them appeared. We will introduce ourselves to integrable systems, and we will describe how the technique of the inverse scattering transform is applied in soliton theory. If time permits, we will give some examples of integrable systems and we will discuss their applications.

4:00PM

** Title: **Solitons and the inverse scattering transform: an overview.

** Abstract: **An exciting and extremely active area of research investigation is the study of solitons and the nonlinear partial differential equations that describe them. In this talk, we will discuss what solitons are, and what makes them so special. We will see when the first solitons were observed, and when the first math that describe them appeared. We will introduce ourselves to integrable systems, and we will describe how the technique of the inverse scattering transform is applied in soliton theory. If time permits, we will give some examples of integrable systems and we will discuss their applications.

Geometry and Topology Seminar**Yvon Verberne (University of Toronto)**

Automorphisms of the fine curve graph

4:00PM, 122 Mathematics Building

Algebra Seminar**Bangming Deng, Tsinghua U**

Fourier transforms on Ringel-Hall algebras

4:00PM, Zoom - contact achirvas@buffalo.edu for link

Applied Math Seminar**Weinan Wang, University of Arizona**

Recent progress on the well-posedness theory for some kinetic models

2:00PM, Math 250 and on Zoom - contact mbichuch@buffalo.edu for link

Geometry and Topology Seminar**Assaf Bar-Natan (Brandeis University)**

How the Thurston metric on Teichmuller space is (not) like L^(infty)

4:00PM, 122 Mathematics Building

Algebra Seminar**Guanglian Zhang, Shanghai Jiao Tong University**

Every type-A quiver locus is a Kazhdan-Lusztig variety

9:00AM, Note unusual time. On Zoom (please email achirvas@buffalo.edu)

Applied Math Seminar**Qingguo Hong, Penn State**

A priori error analysis and greedy training algorithms for neural networks solving PDEs.

2:00PM, Math 250 and on Zoom - contact mbichuch@buffalo.edu for link

Geometry and Topology Seminar**Yuan Yao (UC Berkeley)**

Computing embedded contact homology in Morse-Bott settings

4:00PM, 122 Mathematics Building

Algebra Seminar**Mariusz Tobolski, University of Wroclaw**

Cohomology of free unitary quantum groups

4:00PM, Mathematics Building room 250

In this talk, I will present the Hochschild and bialgebra cohomology with 1-dimensional coefficients of the \(*\)-algebras associated with free universal unitary quantum groups. The result is based on the free resolution of the counit of the free orthogonal quantum groups found by Collins, Härtel, and Thom which was then generalized by Bichon to the case of quantum groups associated with a nondegenerate bilinear form. In fact, we compute cohomology groups of the universal cosovereign Hopf algebras, which generalize free unitary quantum groups and are connected to quantum groups of non-degenerate bilinear forms. This is a joint work with U. Franz, M. Gerhold,A. Wysocza\'nska-Kula, and I. Baraquin.

Algebra Seminar**Robert Corless, Western University**

Bohemian Matrix Geometry

4:00PM, Mathematics Building room 250

A Bohemian matrix family is a set of matrices all of whose entries are drawn from a fixed, usually discrete and hence bounded, subset of a field of characteristic zero. Originally these were integers---hence the name, from the acronym BOunded HEight Matrix of Integers(BOHEMI)---but other kinds of entries are also interesting. Some kinds of questions about Bohemian matrices can be answered by numerical computation, but sometimes exact computation is better. In this paper we explore some Bohemianfamilies (symmetric, upper Hessenberg, or Toeplitz) computationally, and answer some (formerly) open questions posed about the distributions of eigenvalue densities.

This work connects with several disparate areas of mathematics, including dynamical systems, combinatorics, probability and statistics, and number theory. Because the thinking about the topic is so recent, most of the material is still quite exploratory, and this talk will be accessible to students as well as to faculty. Several open problems remain open, and I would welcome your thoughts on them.

This is joint work with several people, including EuniceY.S. Chan, Leili Rafiee Sevyeri, Neil J. Calkin, Piers W. Lawrence, Laureano Gonzalez-Vega, Dan Piponi, Juana Sendra, and Rafael Sendra.

Geometry and Topology Seminar**Nima Hoda (Cornell University)**

Normed polyhedral complexes and nonpositive curvature

4:00PM, 122 Mathematics Building

Algebra Seminar**Jacopo Zanchettin, SISSA**

Hopf algebroids and twists for quantum projectivespaces

4:00PM, Mathematics Building room 250

The Ehresmann-Schauenburg (E-S) bialgebroid associatedwith a Hopf-Galois extension is the noncommutative analog of the gauge groupoidassociated with a principal bundle. As for a Hopf algebra, a Hopf algebroid isa bialgebroid with an invertible antipode. In this talk, after recalling somebasic notions about rings, coring, and bialgebroids, we first show how twists(a sub-group of characters) of a bialgebroid are related to antipodes in thegeneral case. Eventually, after a short introduction to Hopf-Galois extensions,we characterize them for the E-S bialgebroid. Finally, we work out the exampleof a family of \(O(U(1))\)-extensions over quantum projective spaces. This talkis based on joint work with L. Dabrowski and G. Landi arXiv:2302.12073

Geometry and Topology Seminar**Vasudevan Srinivas (Tata Institute)**

What is the Hodge Conjecture?

4:00PM, 122 Mathematics Building

Algebra Seminar**Ana Agore, Max Planck Institut and Simion Stoilow Institute of Mathematics**

Universal constructions for Poisson algebras. Applications.

9:00AM, Zoom (please email achirvas@buffalo.edu)

We introduce the universal algebra of two Poisson algebras \(P\) and \(Q\) as a commutative algebra \(A := \mathcal{P}(P, Q)\) satisfying a certain universal property. The universal algebra is shown to exist for any finite-dimensional Poisson algebra \(P\) and several of its applications are highlighted. For any Poisson \(P\)-module \(U\), we construct a functor \(U\otimes-: {}_A\mathcal{M} \to {}_Q\mathcal{PM}\) from the category of \(A\)-modules to the category of Poisson \(Q\)-modules which has a left adjoint whenever \(U\) is finite-dimensional. Similarly, if \(V\) is an \(A\)-module, then there exists another functor \(-\otimes V:{}_P\mathcal{PM}\to {}_Q\mathcal{QM}\) connecting the categories of Poisson representations of \(P\) and \(Q\) and the latter functor also admits a left adjoint if \(V\) is finite-dimensional. If \(P\) is\(n\)-dimensional, then \(\mathcal{P}(P) := \mathcal{P}(P, P)\) is the initial object in the category of all commutative bialgebras coacting on \(P\). As an algebra,\(\mathcal{P}(P)\) can be described as the quotient of the polynomial algebra\(k[X_{ij} | i, j = 1, · · · , n]\) through an ideal generated by \(2n^3\)non-homogeneous polynomials of degree \(\le 2\). Two applications are provided. The first one describes the automorphisms group\(\mathrm{Aut}_{\mathrm{Poiss}}(P)\) as the group of all invertible group-like elements of the finite dual \(\mathcal{P}(P)^{\circ}\). Secondly, we show that for an abelian group\(G\), all \(G\)-gradings on \(P\) can be explicitly described and classified in terms of the universal coacting bialgebra \(\mathcal{P}(P)\). Joint work with G.Militaru.

Applied Math Seminar**Boaz Ilan, UC Merced**

NLS equations: solitons, dispersive shocks and singularity formation.

2:00PM, Zoom - contact mbichuch@buffalo.edu for link

Analysis Seminar**Min Woong Ahn, SUNY at Buffalo**

The error-sum function of Pierce expansions

4:00PM, 250 Math Building

Colloquium**Bena Tshishiku (Brown University)**

Mapping class groups and Nielsen realization problems

4:00PM, 250 Mathematics Building

Geometry and Topology Seminar**Bena Tshishiku (Brown University)**

Pseudo-Anosov theory in the Goeritz group

4:00PM, 122 Mathematics Building

Algebra Seminar**Michael Brannan, University of Waterloo**

Ulam stability for quantum groups

4:00PM, 250 Mathematics Building

In recent years, there has been a growing interest in the study of approximate representations of various algebraic structures. This is due to some very deep connections with (1) approximation properties for groups and (2) questions about robustness in quantum information theory. The basic question that we are interested in is the following: If we are given a linear map from an algebra (or group) into the bounded operators on a Hilbert space that is “almost” multiplicative, under what conditions can we guarantee that this map is a small perturbation of an actual representation of the algebra? I will describe some of the history around this problem as well as some on going work with Junichiro Matsuda (Kyoto) and Jennifer Zhu (Waterloo), where we investigate the Ulam (=operator norm) stability of approximate representations for compact and discrete quantum groups.

Analysis Seminar**Daxun Wang. SUNY at Buffalo**

Boundary actions of groups and their C*-algebras

4:00PM, 250 Math Building

Geometry and Topology Seminar**Adam Sikora (University at Buffalo)**

On skein modules of rational homology spheres

4:00PM, 122 Mathematics Building

Analysis Seminar**Jintao Deng, SUNY at Buffalo**

The equivariant coarse Baum-Connes conjecture

4:00PM, 250 Mth Building

Colloquium**Demonstration of new GRADER app**

4:00PM, Room 250

Algebra Seminar**Peter Koroteev, University at Buffalo**

Opers and integrability

4:00PM, University at Buffalo, Buffalo, NY 14260, USA

Analysis Seminar**Jintao Deng, SUNY at Buffalo**

The equivariant coarse Baum-Connes conjecture Part II

4:00PM, 250 Math Building

Algebra Seminar**Tomasz Maszczyk, University of Warsaw**

Quantum symmetries of Frobenius algebras

4:00PM, University at Buffalo, Buffalo, NY 14260, USA

Analysis Seminar**Min Woong Ahn, SUNY at Buffalo**

Hausdorff dimensions in Pierce expansions

4:00PM, 250 Math Building

Applied Math Seminar**Jiuhua Hu, University of Wisconsin at Madison**

Wavelet-based Edge Multiscale Parareal Algorithm for Parabolic Equations with Heterogeneous Coefficients.

3:00PM, Math 122 and on Zoom - contact mbichuch@buffalo.edu for link

Algebra Seminar**Gigel Militaru, University of Bucharest**

The set-theoretic quantum Yang-Baxter equation: new perspectives and strategies

4:00PM, Zoom only (please email achirvas@buffalo.edu)

Joint work with Ana Agore and Alexandru Chirvasitu.

Colloquium**Xuhua He, University of Hong Kong**

Machine learningassisted exploration for affine Deligne-Lusztig varieties Speaker host: Yiqiang Li

10:00AM, Via zoom link: https://buffalo.zoom.us/j/98322986435?pwd=OE5OZTVEcE1BZmNuZmYrdmhUNVk4UT09

Speaker: XuhuaHe, University of Hong Kong

Title: Machine learningassisted exploration for affine Deligne-Lusztig varieties

Speaker host: Yiqiang Li

Applied Math Seminar**Ming Zhong, Illinois Institute of Technology**

Learning Collective Behaviors from Observation.

3:00PM, Math 122 and on Zoom - contact mbichuch@buffalo.edu for link

Applied Math Seminar**Nick Moore, Colgate University**

TBA.

3:00PM, Math 122 and on Zoom - contact mbichuch@buffalo.edu for link

Geometry and Topology Seminar**Ivan Dynnikov (Steklov Mathematical Institute of RAS)**

An algorithm for comparing Legendrian links

4:00PM, 122 Mathematics Building

Algebra Seminar**Gurbir Dhillon, Yale**

Sheaves on semi-infinite flag manifolds and Langlands duality Abstract : Let \(G\), \(G^L\) be Langlands-dual reductive groups. The geometric Satake equivalence is the wonderful fact that one can realize the monoidal category of \(G^L\)-representations as a category of constructible sheaves on a space built from \(G\), namely its affine Grassmannian. After recalling this story, we will present similar realizations of the representations of every parabolic and Levi subgroup of \(G^L\) as sheaves on the semi-infinite partial flag manifolds of \(G\). Time permitting, we will describe some natural extensions, including the realizations of the representations of various quantum groups. The contents of this talk build on work and conjectures of many people, notably Arkhipov, Bezrukavnikov, Braverman, Feigin, Finkelberg, Frenkel, Gaitsgory, Lusztig, Mirkovic, Vilonen, and Raskin, and is the subject of work in progress with Campbell, Chen, Lysenko, and Achar-Riche.

4:00PM, Mathematics Building, room 250

Title: Sheaves on semi-infinite flag manifolds and Langlands duality

Abstract : Let \(G\), \(G^L\) be Langlands-dual reductive groups. The geometric Satake equivalence is the wonderful fact that one can realize the monoidal category of \(G^L\)-representations as a category of constructible sheaves on a space built from \(G\), namely its affine Grassmannian. After recalling this story, we will present similar realizations of the representations of every parabolic and Levi subgroup of \(G^L\) as sheaves on the semi-infinite partial flag manifolds of \(G\). Time permitting, we will describe some natural extensions, including the realizations of the representations of various quantum groups.

The contents of this talk build on work and conjectures of many people, notably Arkhipov, Bezrukavnikov, Braverman, Feigin, Finkelberg, Frenkel, Gaitsgory, Lusztig, Mirkovic, Vilonen, and Raskin, and is the subject of work in progress with Campbell, Chen, Lysenko, and Achar-Riche.

Applied Math Seminar**Ruth López Fajardo, Florida State**

From Data to Insights: Permeability Estimation with a Direct Filter

Abstract : In this study, we implement a computational method for the estimation of permeability values within a defined spatial domain based on observed fluid pressure distributions. Our methodology frames the problem as an inverse problem where the Forward Model, responsible for generating the observed data, is solved using a Locally Conservative Enriched Galerkin Solver for Elliptic and Parabolic partial differential equations (PDEs). The parameter estimation process is then addressed with a Bayesian framework, treating it as an on-line problem, which is subsequently solved by the Direct filter method.

2:00PM, Math 122

Analysis Seminar**Francesc Perera, Universitat Autonoma de Barcelona**

Traces on ultrapowers of C*-algebras

4:00PM, 250 Math Building

Colloquium**Lei Yang, Institute for Advanced Study**

Effective versions of Ratner’s equidistribution theorem

4:00PM, Mathematics Building, room 250

Algebra Seminar**Bach Nguyen, Xavier University**

: Poisson geometry and the representation theory of cluster algebras

4:00PM, Mathematics Building room 250

Analysis Seminar**Jinmin Wang, Texas A&M University**

Stoker's problem and index theory on manifolds with polytope singularities

4:00PM, 250 Math Building

Applied Math Seminar**Yijun Sun, UB**

Machine learning approaches to cancer progression modeling and cancer driver gene detection.

3:00PM, Math 122 and on Zoom - contact mbichuch@buffalo.edu for link

Algebra Seminar**Leonid Rybnikov, MIT/Montreal**

The Gaudin model in the Deligne category Rep\(GL_t\)

4:00PM, Mathematics Building Room 250

Applied Math Seminar**Dmitry Pelinovsky, Mcmaster University**

Instability of peaked waves in hydrodynamical models.

3:00PM, Math 122 and on Zoom - contact mbichuch@buffalo.edu for link

Algebra Seminar**Changlong Zhong, Albany**

Elliptic cohomology and the Fourier-Mukai transform

4:00PM, Mathematics Building Room 250

Applied Math Seminar**Giselle Sosa Jones, Oakland University**

Discontinuous Galerkin discretizations of multiphase flow problems in porous media.

3:00PM, Math 122 and on Zoom - contact mbichuch@buffalo.edu for link

Algebra Seminar**Pablo Boixeda Alvarez, Yale**

The center of the small quantum group and affineSpringer fibers Abstract : The quantum group \(U_q\) is a Hopf algebraintroduced by Lusztig deforming the enveloping algebra. The representationtheory of this algebra is particularly interesting at \(l^{th}\) roots of unity,where it includes a finite-dimensional subalgebra known as the small quantumgroup. In joint work with Bezrukavnikov,Shan and Vasserot we construct an injective map to the center of this algebrafrom the cohomology of a certain affine Springer fiber \(\cF{l}_{ts}\) for aregular semisimple element \(s\). In recent progress we check that this map issurjective in type A and get a bound on dimension in general types related tothe diagonal coinvariant algebra. We also give an algebro-geometric descriptionof the spectrum of the cohomology of the Springer fiber. The work relies onunderstanding the representation category through a filtration coming fromintersection with \(G[[t]]\)-orbits in \(\cF{l}_{ts}\) . In this talk I willpresent the result and related properties of this filtration of the category.

4:00PM, Mathematics Building room 250

Speaker: PabloBoixeda Alvarez, Yale

Title: The center of the small quantum group and affineSpringer fibers

Abstract : The quantum group \(U_q\) is a Hopf algebraintroduced by Lusztig deforming the enveloping algebra. The representationtheory of this algebra is particularly interesting at \(l^{th}\) roots of unity,where it includes a finite-dimensional subalgebra known as the small quantumgroup. In joint work with Bezrukavnikov,Shan and Vasserot we construct an injective map to the center of this algebrafrom the cohomology of a certain affine Springer fiber \(\cF{l}_{ts}\) for aregular semisimple element \(s\). In recent progress we check that this map issurjective in type A and get a bound on dimension in general types related tothe diagonal coinvariant algebra. We also give an algebro-geometric descriptionof the spectrum of the cohomology of the Springer fiber. The work relies onunderstanding the representation category through a filtration coming fromintersection with \(G[[t]]\)-orbits in \(\cF{l}_{ts}\) . In this talk I willpresent the result and related properties of this filtration of the category.

Algebra Seminar**Hunter Dinkins, Northeastern**

q-Hypergeometric Functions and the Geometry of Quiver Varieties

4:00PM, Mathematics Building room 250

Algebra Seminar**Yan Soibelman, Kansas State**

Perturbative expansions in Chern-Simons theory from the point of view of Holomorphic Floer Theory

4:00PM, Zoom (please email achirvas@buffalo.edu)

HFT has many applications e.g. the unifying point of view on the Riemann-Hilbert correspondence. I am going to explain an application to exponential integrals in finite and infinite dimensions. In the case of Chern-Simons theory this leads to several interesting conjectures, including the one about the existence of a mixed Hodge structure of infinite rank associated to a complexified Chern-Simons functional.

Applied Math Seminar**Applied Math Seminar: Alexander Korotkevich (UNM)**

Numerical Verification of the 6-Wave 1D Kinetic Equation.Speaker: Alexander Korotkevich (University of New Mexico, Department of Math&Stat)

4:00PM, Zoom

Special Event**Makoto Ozawa (Komazawa University) via Zoom only Friday**

4:00PM

Applied Math Seminar**Applied Math Seminar**

Denis Silantyev (UCCS)

Generalized Constantin-Lax-Majda Equation: Collapse vs. Blow Up and Global ExistenceSpeaker: Denis Silantyev (UC Colorado Springs, Department of Mathematics)

4:00PM, Zoom

Applied Math Seminar**Dr. Kai Yang, Florida International University**

Numerical methods for the KdV-type equations

4:00PM, Zoom: for link see email announcement or contact sergeyd at buffalo dot edu

Colloquium**Cary Malkiewich, Binghamton University**

Brave new fixed-point theory

4:00PM, Zoom: for link see email announcement or contact badzioch at buffalo dot edu

Algebra Seminar**Benjamin Passe, United States Naval Academy**

Boundary representations and isolated points

4:00PM, Zoom. Contact achirvas AT buffalo DOT edu for link.

Applied Math Seminar**Pavel Lushnikov, University of New Mexico**

Conformal mappings and integrability of surface dynamics

4:00PM, Zoom: for link contact sergeyd@buffalo.edu

Geometry and Topology Seminar**Subhankar Dey, University of Alabama**

Detection results in link Floer homology

4:00PM, 122 Mathematics Building

Colloquium**Colloquium: Michael Brannan (University of Waterloo)Via Zoom**

4:00PM

Geometry and Topology Seminar**Hong Chang, University at Buffalo**

Efficient geodesics in the curve complex and their dot graphs

4:00PM, 122 Mathematics Building

Special Event**Colloquium: Gino Biondini, University at Buffalo**

Two adventures in integrable systems: thenonlinear Schrodinger equation with non-trivial boundary conditions

4:00PM, Room 250 Math Building, North Campus

A significant advance in mathematical physics in thesecond half of the twentieth century was the development of the theory ofmodern integrable systems. These systems are nonlinear evolution equations ofphysical significance that provide the nonlinear counterpart to the classicalPDEs of mathematical physics.

One such equation, and in some respects the mostimportant one, is the nonlinear Schrödinger (NLS) equation. The NLS equation isa universal model for weakly nonlinear dispersive wave packets, and arises in avariety of physical settings, including deep water, optics, acoustics, plasmas,condensed matter, etc. In addition, the NLS equation is a completelyintegrable, infinite-dimensional Hamiltonian system, and as a result itpossesses a remarkably deep and beautiful mathematical structure. At the rootof many of these properties is the existence of Lax pair, namely the fact thatthe NLS equation can be written as the compatibility condition of anoverdetermined pair of linear ODEs. The first half of the Lax pair for the NLSequation is the Zakharov-Shabat scattering problem, which is equivalent to aneigenvalue problem for a one-dimensional Dirac operator.

Even though the NLS equation has been extensively studiedthroughout the last sixty years, it continues to reveal new phenomena and offermany surprises. In particular, the focusing NLS equation with nontrivialboundary conditions has received renewed attention in recent years. This talkis devoted to presenting two recent results in this regard. Specifically, Iwill discuss: (i) A characterization of the universal nonlinear stage ofmodulational instability, achieved by studying the long-time asymptotics ofsolutions of the NLS equation with non-zero background; (ii) A characterizationof a two-parameter family of elliptic finite-band potentials of thenon-self-adjoint ZS operator, which are associated with purely real spectrum ofHill’s equation (i.e., the time-independent Schrodinger equation with periodiccoefficients) with a suitable complex potential.

Geometry and Topology Seminar**Sahana Hassan Balasubramanya, University of Münster**

Actions of solvable groups on hyperbolic spaces

4:00PM, Zoom

Algebra Seminar**Xiuping Su, University of Bath**

Kac's Theorem for a class of string algebras of affine type \(\mathbf {C}\).

4:00PM, Contact achirvas@buffalo.edu for zoom link

Applied Math Seminar**Dmitry Zakharov, Central Michigan U**

Lump chains in the KP-I equation

4:00PM, Zoom - contact sergeydy@buffalo.edu for link

Colloquium**Peter Thomas (Case Western U)**

Phase and phase-amplitude reduction for stochastic oscillators

4:00PM, 250 Math Bldg, also accessible via Zoom - contact badzioch@buffalo for link

Geometry and Topology Seminar**Daxun Wang, University at Buffalo**

Boundary action of CAT(0) groups and their \(C^\ast\)-algebras.

4:00PM, 122 Mathematics Building

Applied Math Seminar**Bernard Deconinck, U of Washington**

The water wave pressure problem

4:00PM, Zoom - contact sergeyd@buffalo.edu for link

Geometry and Topology Seminar**Matt Durham, UC Riverside/Cornell University**

Local quasicubicality and sublinear Morse geodesics in mapping class groups and Teichmuller space

4:00PM, 122 Mathematics Building

Algebra Seminar**Daniel Sage, LSU**

The Deligne–Simpson problem for connections on \(\mathbb{G}_m\) with a maximally ramified singularity

4:00PM, Mathematics Building Room 250

Applied Math Seminar**Svetlana Roudenko, Florida International University**

The gKdV world thru the NLS lens

4:00PM, Zoom, contact sergeyd@buffalo.edu for link

Colloquium**Juanita Pinzón Caicedo, University of Notre Dame**

Four-manifolds and knot concordance

4:00PM, 250 Math Bldg. Also via Zoom - contact badzioch@buffalo.edu for link.

Geometry and Topology Seminar**Juanita Pinzon Caicedo, University of Notre Dame**

Satellite Operations that are not homomorphisms.

4:00PM, 122 Mathematics Building

Special Event**Nicolle González, UCLA**

A skein theoretic \(A_{q,t}\) algebra

4:00PM, Mathematics Building room 250

Geometry and Topology Seminar**Ciprian Manolescu, Stanford University**

A knot Floer stable homotopy type

Knot Floer homology (introduced by Ozsváth–Szabó and Rasmussen) is an invariant whose definition is based on symplectic geometry, and whose applications have transformed knot theory over the last two decades. Starting from a grid diagram of a knot, I will explain how to construct a spectrum whose homology is knot Floer homology. Conjecturally, the homotopy type of the spectrum is an invariant of the knot. The construction does not use symplectic geometry, but rather builds on a combinatorial definition of knot Floer homology. We inductively define models for the moduli spaces of pseudo-holomorphic strips and disk bubbles, and patch them together into a framed flow category. The inductive step relies on the vanishing of an obstruction class that takes values in a complex of positive domains with partitions. (This is joint work with Sucharit Sarkar.)

4:00PM, Zoom

Algebra Seminar**Jie Ren, UB**

Quivers and 2-Calabi-Yau categories

4:00PM

The framework of Calabi-Yau categories is appropriate forthe theory of motivic Donaldson-Thomas invariants. I will give an introductionto the Calabi-Yau categories associated to quivers, and the analyticity oftheir stability structures.

Special Event**Jie Ren, UB**

Quivers and 2-Calabi-Yau categories

4:00PM

The framework of Calabi-Yau categories is appropriate forthe theory of motivic Donaldson-Thomas invariants. I will give an introductionto the Calabi-Yau categories associated to quivers, and the analyticity oftheir stability structures.

Applied Math Seminar**Panayotis Kevrekidis, U Mass**

Some Vignettes of Nonlinear Waves in Granular Crystals: From Modeling and Analysis to Computations and Experiments

4:00PM, Zoom - contact sergeyd@buffalo.edu for link

Special Event**Tara Hudson**

12:30PM

Special Event**103 Desk needs to be moved**

12:30PM

Analysis Seminar**Yi Wang, Chongqing University**

__Helton-Howe trace, Connes-Chern character and quantization__

8:00PM, On Zoom - contact hfli@math.buffalo.edu for link

Applied Math Seminar**Maxim Bichuch, SUNY Buffalo**

Introduction to Decentralized Finance

4:00PM, Math 250 and on Zoom - contact mbichuch@buffalo.edu for link

Analysis Seminar**Mariusz Tobolski, University of Wroclaw**

The Stone-von Neumann theorem for locally compact quantum groups

4:00PM, On Zoom - contact hfli@mah.buffalo.edu for link

Geometry and Topology Seminar**Bill Menasco (UB)**

Surface Embeddings in \(\mathbb{R}^2 \times \mathbb{R}\)

4:00PM, 122 Mathematics Building

Algebra Seminar**Shichen Tang**

Arithmetic stability of higher rank Artin-Schreier-Witt towers

4:00PM, 250 Mathematics Building

Analysis Seminar**Hanfeng Li, SUNY at Buffalo**

Entropy and asymptotic pairs

4:00PM, 250 Math Building and on Zoom - contact hfli@buffalo.edu for Zoom link

Geometry and Topology Seminar**Yulan Qing (Fudan University/ University of Toronto)**

Gromov boundary extended

4:00PM, 122 Mathematics Building

Algebra Seminar**Mariusz Tobolski, University of Wrocław**

4:00PM, 250 Mathematics Building

Applied Math Seminar**Yangwen Zhang, CMU**

A new reduced order model of linear parabolic PDEs.

4:00PM, Math 250 and on Zoom - contact mbichuch@buffalo.edu for link

Special Event**250 Sexual Harassment Prevention Training**

5:15PM, 250 Mathematics Building

Colloquium**Abdul Zalloum (University of Toronto)**

4:00PM, 250 Mathematics Building

Geometry and Topology Seminar**Abdul Zalloum (University of Toronto)**

Hyperbolic models for CAT(0) spaces

4:00PM, 122 Mathematics Building

Algebra Seminar**Li Li, Oakland University**

Cluster algebras and Nakajima's graded quivervarieties

4:00PM, 250 Mathematics Building

Nakajima's graded quiver varieties are complex algebraicvarieties associated with quivers. They are introduced by Nakajima in the studyof representations of universal enveloping algebras of Kac-Moody Lie algebras,and can be used to study cluster algebras. In the talk, I will explain how toprecisely locate the supports of the triangular basis of skew-symmetric rank-2quantum cluster algebras by applying the decomposition theorem to variousmorphisms related to quiver varieties, thus prove a conjecture proposed byLee-Li-Rupel-Zelevinsky in 2014.

Special Event**2022 Myhill lecture Series: Gigliola Staffilani October 5-7**

The study of wave interactions: where beautiful mathematical ideas come together.

4:00PM, 250 Mathematics Building,

Applied Math Seminar**Zechuan Zhang, SUNY Buffalo**

Soliton resolution and asymptotic stability of N-soliton solutions for the defocusing mKdV equation with finite density type initial data

4:00PM, Math 250 and on Zoom - contact mbichuch@buffalo.edu for link

Analysis Seminar**Yuqing (Frank) Lin, Texas A&M University**

Entropy for actions of free groups under bounded orbit equivalence

4:00PM, 250 math Building and on Zoom - contact hfli@math.buffalo.edu for link

Geometry and Topology Seminar**Bojun Zhao (UB)**

Left orderability and taut foliations with one-sided branching

4:00PM, 122 Mathematics Building

Algebra Seminar**Mihai Fulger, U of Connecticut**

Positivity vs. semi-stability for bundles with vanishing discriminant

4:00PM, Zoom - contact achirvas@buffalo.edu for link

Colloquium**Jie Shen, Purdue University**

Efficient positivity/bound preserving schemes for complex nonlinear systems

4:00PM, Math Bldg Room 250

Geometry and Topology Seminar**José Román Aranda Cuevas (Binghamton University)**

4:00PM, 122 Mathematics Building

Algebra Seminar**Doyon Kim, Rutgers University**

The existence and uniqueness of Whittaker functionals for \(GL(n,R)\): an algebraic-geometric proof

4:00PM, Zoom; please email achirvas@buffalo.edu for meeting info

Applied Math Seminar**Naoki Masuda, SUNY Buffalo**

Core-periphery structure in networks.

4:00PM, Math 250 and on Zoom - contact mbichuch@buffalo.edu for link

Special Event**Jesse Huang, University of Alberta**

Some attempts to build NCCRs for higher dimensional toric Gorenstein rings

4:00PM, Zoom; please email achirvas@buffalo.edu for meeting info

A noncommutative crepant resolution (NCCR) is a nice endomorphism algebra of a sum of modules that ``resolves'' a normal Gorenstein ring. In the toric context, mirror symmetry suggests that questions surrounding the existence of NCCRs and derived equivalences among them could have geometric answers. In this talk, I will discuss some speculations on a geometric method to construct NCCRs as a quiver algebra for certain toric Calabi-Yau singularities ,potentially generalizing results of Mozgovoy and Bocklandt in dimension 3.

Applied Math Seminar**Scott Rich, Krembil Brain Institute**

Resilience through diversity: Reduced heterogeneity in human epilepsy destabilizes neuronal circuits and promotes seizure-like transitions.

4:00PM, Math 250 and on Zoom - contact mbichuch@buffalo.edu for link

Analysis Seminar**Hongming Nie, SUNY at Stony Brook**

A metric on hyperbolic components

4:00PM, 250 Math Building and on Zoom - contact hfli@math.buffalo.edu for Zoom link

Applied Math Seminar**Anita Layton, Waterloo**

TBA

4:00PM, Zoom - contact mbichuch@buffalo.edu for link

Analysis Seminar**Sagun Chanillo, Rutgers University**

Local Version of Courant's Nodal Domain Theorem

4:00PM, On Zoom - conact hfli@math.buffalo.edu for link

Colloquium**Colloquium Hossein Shahmohamad**

Graphs & Their potent Energy Drinks

4:00PM

Speaker: Hossein Shahmohamad, RIT

Title: Graphs & Their potent Energy Drinks

Geometry and Topology Seminar**Yvon Verberne (University of Toronto)**

Postponed to Spring 2023 due to Storm

Automorphisms of the fine curve graph

4:00PM, 122 Mathematics Building

Analysis Seminar**Joseph Hundley, SUNY at Buffalo**

Functorial Descent in the Exceptional Groups

4:00PM, Zoom - contact hfli@math.buffalo.edu for link

Applied Math Seminar**Weiqi Chu, UCLA**

Non-Markovian opinion models inspired by random processes on networks

4:00PM, Math 250 and on Zoom - contact mbichuch@buffalo.edu for link

Special Event**150 KIm Javor**

10:00AM

Special Event**Liviu Paunescu, Simion Stoilow Institute of Mathematics**

4:00PM, : Zoom; please email achirvas@buffalo.edu for meeting info

Two permutations that almost commute are close to two commuting permutations. The same question can be asked for other relations, not only the commutant. Moreover, the answer to this question depends only on the group that the equations describe. We then survey some recent results where this question is answered affirmatively or negatively, depending on the group, and study the connections to the theory of sofic groups.

**2022 SPOTLIGHT**

INTERDISCIPLINARY EVENT

**UB Biological Sciences Seminar Series**

MARCH 3, 2022; 228 NSC and via Zoom

**Dr. Naoki Masuda, **UB Mathematics, *Gene network analysis: Revealing adaptive structural variants and quantifying omnigenic models. *

- Class of 20216/3/21Four years. You’ve strived, sweated and succeeded. You’ve made friends and memories to last a lifetime. You’ve come so far. To recognize this achievement, the UB Department of Mathematics is pleased to present the name of each graduate in our Class of 2021.
- Class of 20205/14/21
**PRESENTING UB MATHEMATICS CLASS OF 2020.**

Four years. You’ve strived, sweated and succeeded. You’ve made friends and memories to last a lifetime. You’ve come so far. To recognize this achievement, we present the name of each graduate in the Class of 2020.

**Class of 2019:** Professor John Ringland was the faculty speaker at the College of Arts Commencement. Professor Ringland's 2019 Commencement Address is here.

- Myhill Lecture Series 2019: Laura Demarco, Northwestern University9/14/22The Myhill Lecture Series 2019,
*"Complex dynamics and arithmetic geometry"*, will be delivered by Dr. Laura DeMarco, Henry S. Noyes Professor of Mathematics at Northwestern University. She earned her PhD in 2002 from Harvard. DeMarco's research is focused on the dynamics of polynomial or rational mappings on algebraic varieties, especially in dimension 1, with the primary goal of understanding notions of stability and bifurcation. Her recent work explores connections between dynamical properties of maps and the arithmetic geometry of the underlying varieties.

**Dec 3 Algebra Seminar- S. Paul Smith, University of Washington**

Elliptic algebras

4:00PM, Mon Dec 3 2018, 150 Mathematics Bldg.

The algebras of the title form a flat family of (non-commutative!)

deformations of polynomial rings. They depend on a relatively prime

pair of integers n>k>0, an elliptic curve E, and a translation

automorphism of E. Quite a lot is known when n=3 and n=4 (and k=1),

in which case the algebras are deformations of the polynomial ring on

3 and 4 variables. These were discovered and have been closely studied

by Artin, Schelter, Tate, and Van den Bergh, and Sklyanin. They were

defined in full generality by Feigin and Odesskii around 1990 and

apart from their work at that time they have been little studied.

Their representation theory appears to be governed by, and best

understood in terms of, the geometry of embeddings of powers of E (and

related varieties like symmetric powers of E) in projective

spaces. Theta functions in several variables and mysterious identities

involving them provide a powerful technical tool.

This is a report on joint work with Alex Chirvasitu and Ryo Kanda.

- Mark Newman, 20189/14/22Myhill Lecture Series 2018 by Dr. Mark Newman,
*Anatol Rapoport Distinguished University Professor of Physics*, Department of Physics and Center for the Study of Complex Systems, University of Michigan.