Algebra Seminar

Current contacts: Vasily Dolgushev, Ed Letzter or Martin Lorenz.

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.

• Monday April 25, 2022 at 13:30, Wachman 617

  Lie algebras and knots as an excuse

  Vasily Dolgushev, Temple University
  
  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.
  
   

• Thursday September 1, 2022 at 14:00, Wachman 527

  An introduction to the local Langlands correspondence for GL(2)

  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!

   

• Thursday September 8, 2022 at 14:00, Wachman 527

  Overview of representation theory of finite groups

  Martin Lorenz, Temple University
  
  Chapter 1 of A. Prasad's notes.
  
   

• Thursday September 15, 2022 at 14:00, Wachman 527

  Parabolically induced representations of GL2(Fq)

  Nizar Bou Ezz, Temple University
  
  Chapter 2 of A. Prasad's notes.
  
   

• Thursday September 22, 2022 at 14:00, Wachman 527

  The Heisenberg Group and Weil Representation

  Jingfeng Xia, Temple University
  
  Chapter 3.1-3.3 of A. Prasad's notes.
  
   

• Thursday September 29, 2022 at 14:00, Wachman 527

  The Heisenberg Group and Weil Representation II

  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". 
  
   

• Thursday October 6, 2022 at 14:00, Wachman 527

  Constructing cuspidal representations of GL2(Fp)

  Aniruddha Sudarshan, Temple University
  
  Chapter 3.4-3.5 of A. Prasad's notes.
  
   

• Thursday October 13, 2022 at 14:00, Wachman 527

  Constructing the Weil representation from the Heisenberg representation

  Jaclyn Lang, Temple University
  
  I will explain how to construct the Weil representation over a finite field from the Heisenberg representation we have seen in previous talks.
  
   

• Thursday October 20, 2022 at 14:00, Wachman 527

  Smooth representations of locally profinite groups

  Vasily Dolgushev, Temple University

  I will talk about smooth representations of locally profinite groups following the material presented in Chapter 1 of the book "The Local Langlands Conjecture for GL(2)" by Bushnell and Henniart.

   

• Thursday October 27, 2022 at 14:00, Wachman 527

  Smooth representations of locally profinite groups II

  Vasily Dolgushev, Temple University
  
  I will continue talking about smooth representations of locally profinite groups following the material presented in Chapter 1 of the book "The Local Langlands Conjecture for GL(2)" by Bushnell and Henniart. In particular, I will talk about smooth induction and smooth induction with compact supports.
  
   

• Thursday November 10, 2022 at 14:00, Wachman 617

  Measures and Duality

  Nizar Bou Ezz, Temple University
  
  I will talk about the material of Section 3 "Measures and Duality" from Chapter 1 of the book "The Local Langlands Conjecture for GL(2)" by Bushnell and Henniart. 
  
   

• Thursday December 1, 2022 at 14:00, Wachman 617

  Mackey's irreducibility criterion for smooth representations

  Jaclyn Lang, Temple University
  
  I will give a proof of Mackey's irreducibility criterion for smooth representations.  This ties up (most of) our construction of some supercuspidal representations of GL2(Qp).