The Seminar usually takes place on Mondays at 1:30 PM in Room 617 on the sixth floor of Wachman Hall. Click on title for abstract.
I hope that Dror Bar-Natan will forgive me for "stealing" one of his quotes and turning it into a title of this talk... Well, the goal of my talk is to advertise a graduate course that I would like to teach during the fall semester of 2022. This course is divided into two parts.
The first part will be devoted the standard toolbox of Lie theory and the second part will be devoted to applications of Lie algebras to finite type invariants of knots.
In my talk, I will define a Lie algebra, give several examples of Lie algebras and formulate Lie's theorem and Cartan's theorem. Then I will talk about objects related to finite type invariants of knots: chord diagrams, open and closed Jacobi diagrams. If time permits, I will also talk about "links" between these objects. Surely, I will not have time to explain how all the objects are related to Lie algebras. So I hope that... this will be a great incentive to take my graduate course (Math 9100) in the fall.
Jaclyn Lang, Temple University
This talk will introduce the topic of the Algebra Seminar for Fall 2022. The goal is to learn about the objects involved in the local Langlands correspondence for GL(2) through some simple examples, state classifications of these objects, and then explain how they match up under local Langlands. I'll start by sketching what the two sides of the correspondence are, how they arise naturally, and end with a plan for the seminar. Anyone interested in participating in the seminar is encouraged to attend and volunteer for a talk!
Chapter 1 of A. Prasad's notes.
Chapter 2 of A. Prasad's notes.
Chapter 3.1-3.3 of A. Prasad's notes.
Vasily Dolgushev, Temple University
I will continue presenting the material of Chapter 3.1-3.3 from A. Prasad's notes.
I am also going to mention constructions from Chapter 3 of Charlotte Chan's undergraduate
thesis "The Weil Representation".
Chapter 3.4-3.5 of A. Prasad's notes.