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SUMMARY:Instanton Slices [MPIM]
DTSTART:20260820T130000Z
DTEND:20260820T140000Z
DTSTAMP:20260813T172700Z
UID:indico-event-1536@math-events.uni-bonn.de
DESCRIPTION:Speakers: Ivan Cherednik (University of North Carolina at Chap
 el Hill/MPIM)\n\nMPI-Oberseminar\nAcquiring geometric information about al
 gebraic varieties via counting Fq​-points and employing various p-adic 
 techniqueshas always been a challenge\, classically and neoclassically (..
 .\, perfectoid spaces). Surprisingly\, this can be done forS3∖K for cert
 ain(!) hyperbolic knots\, including the famous K12n242\, which approach re
 quiresinstanton slices. These are Quot-stacks of torsion-free modules over
  isolated singularities with prescribed conductors\,in general.I will begi
 n with major theories of superpolynomials and the connection conjectures\,
  focusing on the motivic superpolynomials ofplane curve singularities\, co
 unterparts of the corresponding L-functions. They fully capture topologica
 l types of such singularities.Generally\, L-functions are insufficient to 
 recover the underlining objects\, which seems different in topology of iso
 lated singularities.The main theorem will state that the superpolynomials 
 of instanton slices for Fq[[x\,y]] (non-singular)  and proper conductorsa
 re sufficient to obtain motivic superpolynomials of plane curves singulari
 ties in arbitrary rank\, those due to Ch. Philipp.We will then explain how
  hyperbolic knots enter this theory.In general\, instanton slices are not
  related to "curves"\, which dominate modern geometric representation theo
 ry and its applications.Moreover\, the core constructions are fully applic
 able to char=0\, the case of mixed characteristics.The ref. is arxiv.org/a
 bs/2607.25666\, which also contains the DAHA direction and applications to
  Nekrasov's instanton sums.\n\nhttps://math-events.uni-bonn.de/event/1536/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/1536/
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