Algebraic Geometry Seminar: "Wall-crossing in the McKay correspondence"
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. One can often realise all such minimal resolutions as natural GIT quotients - e.g. when G is an abelian or polyhedral subgroup of SL(3) - although the GIT chamber structure and wall-crossing tend to be relatively poorly understood. I will describe my recent work giving explicit representation-theoretic descriptions of the walls and wall-crossing behaviour for the principal chamber, and discuss current joint work with Tom Ducat (Imperial) connecting wall-crossing to mutations of quivers and (generalised) cluster algebras.
Host: Matt Kerr