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Geometry
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Ben Wormleighton, RLM 9.166: McKay correspondence and walls for G-Hilb
Thursday, January 23, 2020, 03:30pm - 04:30pm
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 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.
Location: RLM 9.166

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