February 3, 2020
Speaker: Franco Rota
Title: Mukai implies McKay
Abstract: What do representations of subgroups of SL(2,C), chains of rational curves and quiver representations have in common? But a Dynkin diagram of course! (and, a triangulated category...) We'll talk about the classical McKay correspondence, and Bridgeland, King and Reid's modern take on it via Fourier-Mukai equivalences. I'll follow parts of the survey "Explicit methods for derived categories of sheaves" by A. Craw
February 20, 2020
Speaker: Yael Davidov
Title: Group Cohomology, what is it good for? Is it good for things? Let's find out!
Abstract: In this talk I will define group cohomology. I will then state (and occasionally prove) some basic properties of the cohomology groups we defined and then we will attempt to "prove" Hilbert's theorem 90 through the lens of the first cohomology group. I will not be assuming any knowledge outside of first year algebra, so hopefully the talk will be very accessible.
February 27, 2020
Speaker: Songhao Zhu
Title: Let's Doodle Dynkin Diagrams!
Abstract: We will try to give an overview on a quick way to classify all the simple Lie algebras over \mathbb{R} using Vogan/Knapp's method of decorating the well-known Dynkin diagrams, which help to classify all the simple Lie algebras over \mathbb{C}. We will review some basic facts of the complex classification. A few easy examples will be discussed. And a few (I mean type A) diagrams will be doodled.
March 5, 2020
Speaker: Edna Jones
Title: Clifford algebras and Mobius transformations
Abstract: I will talk about Clifford algebras and how we can use them to create Mobius transformations in hyperbolic n-space.