Steve Rayan, University of Saskatchewan
"Resolutions of finite quotient singularities and quiver varieties"
Finite quotient singularities play a distinguished role in mathematics, intertwining algebraic geometry, hyperkähler geometry, representation theory, and integrable systems. I will explain the correspondences at play here and how they culminate in Nakajima quiver varieties, which are of intense interest in geometric representation theory and physics. I will explain some recent work of G. Bellamy, A. Craw, T. Schedler, H. Weiss, and myself in which we show that, remarkably, all of the resolutions of a particular finite quotient singularity are realized by a certain Nakajima quiver variety, namely that of the 4-pointed star-shaped quiver. I will place this work in the wider context of the search for McKay-type correspondences for finite subgroups of SL(n,C) on the one hand, and of the construction of finite-dimensional approximations to meromorphic Hitchin systems and their hyperkähler metrics on the other hand. The Hitchin system perspective draws upon my joint work with J. Fisher L. Schaponsik, respectively. Time permitting, I will speculate upon the symplectic duality of Higgs and Coulomb branches in this setting.
MC 5417