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SUMMARY:Anton Mellit (University of Vienna)
DTSTART:20210407T203000Z
DTEND:20210407T213000Z
DTSTAMP:20260423T035531Z
UID:MITLie/26
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/26/">
 Macdonald polynomials and counting parabolic bundles</a>\nby Anton Mellit 
 (University of Vienna) as part of MIT Lie groups seminar\n\nLecture held i
 n 2-142.\n\nAbstract\nIt is well known that Hall-Littlewood polynomials na
 turally arise from the problem of counting partial flags preserved by a ni
 lpotent matrix over a finite field. I give an explicit interpretation of t
 he modified Macdonald polynomials in a similar spirit\, via counting parab
 olic bundles with nilpotent endomorphism over a curve over finite field. T
 he result can also be interpreted as a formula for a certain truncated wei
 ghted counting of points in the affine Springer fiber over a constant nilp
 otent matrix. This leads to a confirmation of a conjecture of Hausel\, Let
 ellier and Rodriguez-Villegas about Poincare polynomials of character vari
 eties. On the other hand\, it naturally leads to interesting expansions of
  Macdonald polynomials and related generating functions that appear in the
  shuffle conjecture and its generalizations.\n
LOCATION:https://researchseminars.org/talk/MITLie/26/
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