##### Department of Mathematics,

University of California San Diego

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### Math 295 - Mathematics Colloquium

## Fernando Rodriguez Villegas

#### UT Austin

## Combinatorics and Geometry

##### Abstract:

In this talk I will discuss a combinatorial calculation of the polynomial that counts the number of indecomposable representations of a certain quiver and dimension vector. I will start by introducing quivers, their representations and Kac's results and conjectures on such counting polynomials in general. The combinatorial calculation involves the reliability polynomial of alternating graphs. I will end with the main motivation for the calculation: its relation to the geometry of character varieties.

Host: Kiran Kedlaya

### February 23, 2012

### 3:00 PM

### AP&M 6402

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