Fri, Mar 31

Geometry and Topology Seminar
Yuan Yao (UC Berkeley)
TBA
4:00PM, 122 Mathematics Building

TBA

Mon, Apr 3

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.

Mon, Apr 10

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.

Fri, Apr 14

Geometry and Topology Seminar
Nima Hoda (Cornell University)
TBA
4:00PM, 122 Mathematics Building

TBA

Mon, Apr 24

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.

Mon, Apr 24

Applied Math Seminar
Boaz Ilan, UC Merced
TBA

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

TBA

Thu, Apr 27

Colloquium
Bena Tshishiku (Brown University)

4:00PM, 250 Mathematics Building

Buffalo Spring Lectures in Geometry and Topology

Fri, Apr 28

Geometry and Topology Seminar
Bena Tshishiku (Brown University)

4:00PM, 122 Mathematics Building

Buffalo Spring Lectures in Geometry and Topology

Fri, May 12

Geometry and Topology Seminar
Reserved
4:00PM, 122 Mathematics Building