##### Department of Mathematics,

University of California San Diego

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### Special Colloquium

## Aaron Lauda

#### University of Columbia

## Categorifying Quantum Groups and Link Invariants

##### Abstract:

\indent The Jones polynomial can be understood in terms of the representation theory of the quantum group associated to $sl2$. This description facilitated a vast generalization of the Jones polynomial to other quantum link and tangle invariants called Reshetikhin-Turaev invariants. These invariants, which arise from representations of quantum groups associated to simple Lie algebras, subsequently led to the definition of quantum 3-manifold invariants. In this talk we categorify quantum groups using a simple diagrammatic calculus that requires no previous knowledge of quantum groups. These diagrammatically categorified quantum groups not only lead to a representation theoretic explanation of Khovanov homology but also inspired Webster's recent work categorifying all Reshetikhin-Turaev invariants of tangles.

### January 18, 2011

### 1:00 PM

### AP&M 6402

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