# Seminar : Basic Aspects of Representation Theory (BART)

This is the page for the weekly seminar organized by a group of postdocs and graduate students working on representation theory and related fields at SNU in 2014.

## Contents

## Spring 2014

We usually meet at 2-3:30pm.

### 4/2 (129-406)

Chul-hee Lee, On Chevalley's integral forms for simple Lie algebras

integral forms of Chevalley and Kostant

### 4/9 (129-301)

UhiRinn Suh, Drinfel'd-Sokolov reduction and W-algebras

Lax operators, Drinfel'd-Sokolov reduction, affine classical W-algebras, finite classical W-algebras

### 4/16 (27-220)

Jonathan Axtell, Affine vertex algebras

definitions, Zhu's algebra and classification of simple modules

### 4/23 (129-310)

Ji Hye Jung, Schur algebras

polynomial representations of $\rm GL_n$ and Schur algebras

### 4/30 (129-406)

HyunKyu Kim (KIAS), Representations of quantum plane algebra

definition, tensor product decomposition, pentagon equation, quantum Teichmüller theory

### 5/7 (129-406)

Dongwoo Kim, Schur-Weyl duality

### 5/14 (129-406)

Jonathan Axtell, Schur and Weyl modules

### 5/21 (129-406)

Chul-hee Lee, Cube root of the $j$-invariant and $E_8$

### 5/28

Hyoungju Park, Crystal bases

### 6/3

Seok-Jin Kang

**Please be aware of the date and time change.** It will be held on Tuesday at 16:00.

### 7/2

Chul-hee Lee, Linear recurrence relations in Q-systems

### 7/29 (129-406, 10-12AM)

Philsang Yoo (Northwestern University) : The best hope for the geometric Langlands program

Abstract : The Langlands correspondence is a deep statement relating number theory and harmonic analysis in a rather unexpected way. It is still largely conjectural for number fields but a lot is known for function fields, not least because one has more algebro-geometric tools over a function field. The geometric Langlands program is in a sense even further simplification by working over the complex number C. The goal of this introductory talk is to state the best hope conjecture of geometric Langlands program from a natural context in terms of categorical harmonic analysis. One should note that we only aim to give some idea of the subject and in particular the version of the conjecture we will see in the talk is known to be wrong.

### ???

Introduction to categorifications (tentative)