GARTS Fall 2024

Sept. 16, 2024

Speaker: Sumit Singh

Title: Introduction to Lie algebras and representation theory

Abstract: I will talk about the Lie algebra sl(2,C). The structure and representation theory of sl(2,C) illuminates the general theory of semisimple Lie algebras. The talk will be based on Humphreys's book.

Sept. 23, 2024

Speaker: Carlos Tapp Monfort

Title: Group Representation Theory

Abstract: I will present the basics of group representation theory. I will define representation and cover the most elementary tools such as Maschke's Theorem. After that I will talk about the character table. My emphasis will be on how the table provides a lot of information about the group, finally I will try to sketch a proof of Burnside's (p^a)(q^b) theorem.

Sept. 30, 2024

Speaker: Alex Day

Title: Modular Group Representation Theory

Abstract: I will present some of the core results of modular representation theory. We will see that for modular representations we have similar but usually weaker analogues of results in the characteristic 0 case, including: Clifford's theorem instead of Maschke's, Brauer's theorem on the number of irreducible representations, and Brauer characters instead of usual ones. I will finish by presenting an application of modular representation theory to a group-theoretic result of Nikolov, Segal and AbĂ©rt (which was the focus of my Master's dissertation).

Oct. 28, 2024

Speaker: Dr. Forrest Thurman

Title: Lambda-rings and Plethysm

Abstract: Let S(R) be the set of formal power series over R with constant coefficient 1. S(R) can be given a ring structure in which addition is the standard product on formal power series. A Lambda-ring will be defined as a ring R equipped with a section to S(R). Lambda-rings are quite ubiquitous and appear whenever there is a notion of exterior power on elements of a ring. We will see what this has to do with symmetric functions, number theory, and the plethysm operation from representations of GL(n).

Nov. 4, 2024

Speaker: Dan Tan

Title: Representations of vertex operator algebras and conformal field theory

Abstract: Vertex operator algebras are infinite dimensional algebras with infinitely many operations. While their axioms are notoriously hard to write down, the main ideas are easily motivated by the physical notion of a conformal field theory. In this talk, we will introduce the notion of a (chiral) conformal field theory and explain how it relates to the representation theory of vertex operator algebras. The example of a free bosonic string will be given to illustrate the main ideas. You don't need to know any of these words to attend!

Nov. 11, 2024

Speaker: Nick Backes

Title: TBD

Abstract: TBD

Nov. 18, 2024

Speaker: Hong Chen

Title: Schur functions(TBD)

Abstract: TBD

Spring 2021 Talks (Jason Saied)

Spring 2019 Talks (Alejandro Ginory)