UCR Graduate Student Representation Theory Seminar
This is the website for the grad-student run Graduate Student Representation Theory Seminar (GSRTS) at UC Riverside, which meets on Thursdays from 12:30-1:50pm. If you wish to attend, please contact Raymond Matson (email located at the bottom of the page) for any questions or comments concerning the seminar.
GSRTS is an extension of the Lie Theory Seminar that is run on Tuesdays from 12:30-1:50pm. The website for that seminar is available at here.
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- March 2, 2023: Vidur Sury
- Title: Matrix Uploaded
- Abstract: We fasten our seat belts and take a breezy journey through the world of matrix groups. Groups of matrices being so ubiquitous in mathematics as well as in other sciences, we focus only on a few aspects such as: (i) decomposition theorems (Iwasawa, Bruhat etc.) of matrix groups, (ii) symmetry groups of Platonic solids, (iii) freedom of groups and a remarkable theorem of Jacques Tits, (iv) Gromov's theorem on `word growth', and (v) subgroup growth. Each of these facets reflects diverse aspects.
- February 16, 2023: Anthony Muljat
- Title: Representation stability for FI-modules and some analogues
- Abstract: The notion of representation stability emerged in the last decade as a means to understand the limiting behavior of certain naturally-arising sequences of representations of finite groups. The idea is to describe such a sequence as a single algebraic object, namely a “category module” for a suitably chosen category. The limiting behavior of this sequence may then be explained in terms of a single finite generation property of the corresponding category module. I will give an overview of the classical case where the category in question is that of finite sets and injective maps (FI), highlighting the implications for homological stability of the symmetric groups with twisted coefficients. Then, I will discuss ongoing work extending these results to other categories and analogous twisted group homologies.
- February 9, 2023: Raymond Matson
- Title: Approaches To Hecke Algebras
- Abstract: Hecke algebras are fascinating and powerful tools used throughout representation theory. I will define Hecke algebras through construction and provide a diagrammatic understanding to their properties. We'll then journey to their affine cousins (and second cousins), affine Hecke algebras and double affine Hecke algebras. The goal of this talk is to introduce all three objects and hopefully provide a reasonable feel of how they work and where they all come from.