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SUMMARY:Harder-Narasimhan stratifications   for decorated principal bundle
 s - Daniel Halpern-Leistner (Cornell University)
DTSTART:20240619T143000Z
DTEND:20240619T153000Z
UID:TALK217708@talks.cam.ac.uk
DESCRIPTION:Harder-Narasimhan (HN) theory gives a structure theorem for pr
 incipal G bundles on a smooth projective curve. A bundle is either semista
 ble\, or it admits a canonical filtration whose associated graded bundle i
 s semistable in a graded sense. After reviewing recent advances in extendi
 ng HN theory to arbitrary algebraic stacks\, I will discuss work with Andr
 es Fernandez Herrero applying this general machinery to the stack of maps 
 from a curve C to a quotient stack X/G\, where G is a reductive group and 
 X is an affine G-scheme. Our main immediate application is to compute gene
 rating functions for K-theoretic gauged Gromov-Witten invariants. The meth
 od we develop to analyze this moduli problem is an infinite dimensional an
 alog of geometric invariant theory\, which is potentially applicable to a 
 much broader range of moduli problems.
LOCATION:Seminar Room 1\, Newton Institute
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