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SUMMARY:Jørgen Rennemo (University of Oslo)
DTSTART:20210126T160000Z
DTEND:20210126T170000Z
DTSTAMP:20260423T004512Z
UID:DerSem/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/DerSem/4/">K
 -theorietic sheaf-counting invariants of Quot^n(C^4)</a>\nby Jørgen Renne
 mo (University of Oslo) as part of Derived seminar\n\n\nAbstract\nConsider
  the Quot scheme parametrising length n quotients of the rank r trivial bu
 ndle on C^4. There's a natural torus action on this scheme\, for which the
  fix points are labelled by r-tuples of solid partitions of total size n. 
 Nekrasov and Piazzalunga have assigned rational function weights to these 
 fix points and conjectured a formula for the generating function of weight
 ed counts of fix points. Oh and Thomas have defined general K-theoretic sh
 eaf counting invariants for Calabi-Yau 4-folds and proved a torus localisa
 tion formula for these. We show that Nekrasov-Piazzalunga's weights agree 
 with weights coming from the Oh-Thomas localisation formula (matching up t
 he signs is the tricky part). We use this to prove that Nekrasov-Piazzalun
 ga's conjectured formula for the generating function is correct. This is j
 oint work with Martijn Kool.\n
LOCATION:https://researchseminars.org/talk/DerSem/4/
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