##### Department of Mathematics,

University of California San Diego

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### AWM Colloquium

## Monica Vazirani

#### University of California, Davis

## Categorifying Quantum Groups

##### Abstract:

What is categorification? If you de-categorify Vector-Spaces, you replace isomorphism classes of objects with natural numbers (their dimensions), replace direct sum with addition of those numbers, and replace tensor product with multiplication. To categorify is to undo this process--for instance, one might start with the ring of symmetric functions and realize it has replaced the representation theory of the symmetric group. In this talk, I will discuss how Khovanov-Lauda-Rouquier (KLR) algebras categorify quantum groups. I will discuss their simple modules, and in particular that they carry the structure of a crystal graph. This is joint work with Aaron Lauda.

Host: AWM

### May 2, 2012

### 2:00 PM

### AP&M 6402

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