Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.


Past events in this series

Mon, 12 Jun 2023

Resolutions of finite quotient singularities and quiver varieties

Steven Rayan
(quanTA Centre / University of Saskatchewan)

Finite quotient singularities have a long history in mathematics, intertwining algebraic geometry, hyperkähler geometry, representation theory, and integrable systems.  I will highlight the correspondences at play here and how they culminate in Nakajima quiver varieties, which continue to attract interest in geometric representation theory and physics.  I will motivate 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 5-pointed star-shaped quiver.  I will place this work in the wider context of the search for McKay-type correspondences for finite subgroups of $\mathrm{SL}(n,\mathbb{C})$ on the one hand, and of the construction of finite-dimensional-quotient approximations to meromorphic Hitchin systems and their integrable systems on the other hand.  The Hitchin system perspective draws upon my prior joint works with each of J. Fisher and L. Schaposnik, respectively. Time permitting, I will speculate upon the symplectic duality of Higgs and Coulomb branches in this setting.