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DTSTART:20230312T070000
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DTSTART;TZID=America/Toronto:20230427T143000
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URL:https://uwaterloo.ca/pure-mathematics-geometry-topology/events/resoluti
 ons-finite-quotient-singularities-and-quiver
SUMMARY:Resolutions of finite quotient singularities and quiver varieties
CLASS:PUBLIC
DESCRIPTION:STEVE RAYAN\, UNIVERSITY OF SASKATCHEWAN\n\nFinite quotient sin
 gularities play a distinguished role in\nmathematics\, intertwining algebr
 aic geometry\, hyperkähler geometry\,\nrepresentation theory\, and integr
 able systems.  I will explain the\ncorrespondences at play here and how t
 hey culminate in Nakajima quiver\nvarieties\, which are of intense interes
 t in geometric representation\ntheory and physics.  I will explain some r
 ecent work of G. Bellamy\,\nA. Craw\, T. Schedler\, H. Weiss\, and myself 
 in which we show that\,\nremarkably\, all of the resolutions of a particul
 ar finite quotient\nsingularity are realized by a certain Nakajima quiver 
 variety\, namely\nthat of the 4-pointed star-shaped quiver.  I will place
  this work in\nthe wider context of the search for McKay-type corresponden
 ces for\nfinite subgroups of SL(n\,C) on the one hand\, and of the constru
 ction\nof finite-dimensional approximations to meromorphic Hitchin systems
 \nand their hyperkähler metrics on the other hand.  The Hitchin system\n
 perspective draws upon my joint work with J. Fisher L. Schaponsik\,\nrespe
 ctively. Time permitting\, I will speculate upon the symplectic\nduality o
 f Higgs and Coulomb branches in this setting.\n\nMC 5417
DTSTAMP:20260312T181029Z
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