Feb. 6, 2023
Speaker: Songhao Zhu
Title: An overview of Lie Superalgebras
Abstract: We will take a look at the Lie objects in the category of vector superspace, i.e., what our organizer emeritus wasted his Ph.D. on. I will briefly review Lie algebras and discuss linear superalgebra as the background. Still, the zoo of simple Lie superalgebras is going to be a wild safari. If time allows, I will say a few things on supersymmetry and my work.
SlidesFeb. 24, 2023
Speaker: Nicholas Backes
Title: Kirillov Models of p-adic Representations
Abstract: The Kirillov model is a way of taking irreducible representations of GL(n, F) and realizing them as representations on a vector space of complex functions on the base field F. Among other uses, the Kirillov model is one way to define Whittaker functions. Properties of the Kirillov model can determine if a representation is cuspidal. For this talk, the base field F will be the p-adic numbers. We will discuss some properties and uses of the Kirillov model, and depending on available time we will discuss some aspects of its construction.
Mar. 3, 2023
Speaker: Jason Saied (KBR, Inc. at NASA Ames Research Center)
Title: Examples of algebra and representation theory in quantum computing
Abstract: A quantum computer is a computer that takes advantage of quantum mechanical properties, generally with the goal of someday performing certain computations faster than classical computers can. I will give an overview of some basic notions in quantum computing, then discuss several places in which algebra and representation theory appear in that field. We will study the Pauli and Clifford groups, their importance, and their relation to several groups of interest to representation theorists. We will then discuss character randomized benchmarking, a technique that uses group character theory to determine the fidelity of real-world implementations of ideal quantum gates.
Fall 2022 Talks (Songhao)
Spring 2021 Talks (Jason Saied)