##### Department of Mathematics,

University of California San Diego

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### Math 208 - Algebraic Geometry

## Ben Wormleighton

#### UC Berkeley

## McKay correspondence and walls for G-Hilb

##### Abstract:

The McKay correspondence takes many guises but at its core connects the geometry of minimal resolutions for quotient singularities $C^n / G$ to the representation theory of the group $G$. When $G$ is an abelian subgroup of $SL(3)$, Craw-Ishii showed that every minimal resolution can be realised as a moduli space of stable quiver representations naturally associated to $G$, although the chamber structure for the stability parameter and associated wall-crossing behaviour is poorly understood. I will describe my recent work giving explicit representation-theoretic descriptions of the walls and wall-crossing behaviour for the chamber corresponding to a particular minimal resolution called the G-Hilbert scheme. Time permitting, I will also discuss ongoing work with Yukari Ito (IPMU) and Tom Ducat (Bristol) to better understand the geometry, chambers, and corresponding representation theory for other minimal resolutions.

Host: Steven Sam

### December 6, 2019

### 12:45 PM

### AP&M 6402

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