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SUMMARY:Daniel Halpern-Leistner (Cornell)
DTSTART:20220411T190000Z
DTEND:20220411T200000Z
DTSTAMP:20260423T021442Z
UID:WHCGP/53
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WHCGP/53/">I
 nfinite dimensional geometric invariant theory and gauged Gromov-Witten th
 eory</a>\nby Daniel Halpern-Leistner (Cornell) as part of Western Hemisphe
 re colloquium on geometry and physics\n\n\nAbstract\nHarder-Narasimhan (HN
 ) theory gives a structure theorem for holomorphic vector bundles on a Rie
 mann surface. A bundle is either semistable\, or it admits a canonical fil
 tration whose associated graded bundle is semistable in a graded sense. Af
 ter reviewing recent advances in extending HN theory to arbitrary moduli p
 roblems in algebraic geometry I will discuss work in progress with Andres 
 Fernandez Herrero and Eduardo Gonzalez to apply this general machinery to 
 the moduli problem of gauged maps from a curve C to a G-variety X\, where 
 G is a reductive group. Our main immediate application is to use HN theory
  for gauged maps to compute generating functions for K-theoretic gauged Gr
 omov-Witten invariants. This problem is interesting more broadly because i
 t can be formulated as an example of an infinite dimensional analog of the
  usual set up of geometric invariant theory\, which has applications to ot
 her moduli problems.\n
LOCATION:https://researchseminars.org/talk/WHCGP/53/
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