Back to Algebraic Geometry Seminar: Spring 2020
Algebraic Geometry Seminar
Date: Tuesday, Feb 11, 2020
Time: 3:30PM - 4:30PM
Location: LCB 222
(special time and place: 1:30-2:30 in JWB 208)
Ben Wormleighton
UC Berkeley
Title |
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 relatively poorly understood. I will describe 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 (Imperial) to better understand the geometry, chambers, and corresponding representation theory for other minimal resolutions. |
Algebraic Geometry