University of California, San Diego.

Date  Speaker  Topic 
October 24, 2022 
Dan Rogalski
UCSD 
Artin Schelter regular algebras
Abstract: What are the noncommutative rings that are most analogous to polynomial rings? One class of such rings are the regular algebras first defined by Artin and Schelter in 1987. Since then such algebras have been extensively studied. We give a survey of these interesting examples and their associated projective geometry.

November 7, 2022 
Gil Goffer
UCSD 
The space of closed subgroups
Abstract: Given a topological group G, one considers the space of its closed subgroups, called the Chabauty space. I will talk about the structure and features of this space, and show how various algebraic and topological properties of a group are expressed there.

November 14, 2022 
Alireza Salehi Golsefidy
UCSD 
Randomwalks in group extensions
Abstract: Basics of randomwalks in a finite group, superapproximation, and recent developments in this subject will be discussed. (More recent results are parts of my joint works with Srivatsa Srinivas.)

November 28, 2022 
Hans Wenzl
UCSD 
Tensor Categories
Abstract: Tensor categories have played an important role in areas as diverse as topology, mathematical physics, operator algebras and representation theory. This is an introductory talk. I will mostly talk about classification of tensor categories with given tensor product rules and module categories for certain important examples.

Date  Speaker  Topic 
January 30, 2023 
Be'eri Greenfeld
UCSD 
Growth of infinitedimensional algebras, symbolic dynamics and amenability
Abstract: The growth of an infinitedimensional algebra is a fundamental tool to measure its infinitude. Growth of noncommutative algebras plays an important role in noncommutative geometry, representation theory, differential algebraic geometry, symbolic dynamics and various recent homological stability results in number theory and arithmetic geometry. We analyze the space of growth functions of algebras, answering a question of Zelmanov (2017) on the existence of certain 'holes' in this space, and prove a strong quantitative version of the Kurosh Problem on algebraic algebras. We use minimal subshifts with highly correlated oscillating complexities to resolve a question posed by KrempaOkninski (1987) and KrauseLenagan (2000) on the GKdimension of tensor products. An important property implied by subexponential growth (for both groups and algebras) is amenability. We show that minimal subshifts of positive entropy give rise to amenable graded algebras of exponential growth, answering a conjecture of Bartholdi (2007; naturally extending a wide open conjecture of Vershik on amenable group rings). This talk is partially based on joint works with J. Bell and with E. Zelmanov.

February 6, 2023 
Pablo Ocal
UCLA 
A twisted approach to the Balmer spectrum of the stable module category of a Hopf algebra
Abstract: The Balmer spectrum of a tensor triangulated category is a topological tool analogous to the usual spectrum of a commutative ring. It provides a universal theory of support, giving a categorical framework to (among others) the support varieties that have been used to great effect in modular representation theory. In this talk I will present an approach to the Balmer spectrum of the stable module category of a Hopf algebra using twisted tensor products and emphasizing examples. This will include an unpretentious introduction to twisted tensor products, the Balmer spectrum, and the relevance of both in representation theory.

March 13, 2023 
Cris Negron
USC 
TBA
Abstract:
