University of California, San Diego.
Academic year: 2022-2023.
Monday 3:00-4:00, 7321 AP&M
Questions? email Dan Rogalski at

Fall 2022

Date Speaker Topic
October 24, 2022 Dan Rogalski
  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
  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
  Random-walks in group extensions

  Abstract: Basics of random-walks in a finite group, super-approximation, 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
  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.

Winter 2023

Date Speaker Topic
January 30, 2023 Be'eri Greenfeld
  Growth of infinite-dimensional algebras, symbolic dynamics and amenability

  Abstract: The growth of an infinite-dimensional 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 Krempa-Okninski (1987) and Krause-Lenagan (2000) on the GK-dimension 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
  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