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SUMMARY:Kaif Hilman (University of Bonn)
DTSTART:20250903T080000Z
DTEND:20250903T093000Z
DTSTAMP:20260422T161058Z
UID:HKUST-AG/78
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/HKUST-AG/78/
 ">Atiyah-Bott's fixed point theorem via categorification</a>\nby Kaif Hilm
 an (University of Bonn) as part of Algebra and Geometry Seminar @ HKUST\n\
 nLecture held in Room 4472 (Lift 25/26).\n\nAbstract\nA famous result of A
 tiyah and Bott in geometric topology says that a smooth action by a cyclic
  p-group on a smooth closed orientable manifold cannot have just a single 
 fixed point when p is an odd prime. This result was proved using the Atiya
 h-Singer index theorem. In this talk\, I will explain a different\, purely
  homotopical\, proof which in particular exhibits that the theorem is real
 ly a consequence of ``global'' homotopical reasons rather than ``local'' g
 eometric ones. To this end\, I will introduce a theory of Poincare duality
  for arbitrary topoi together with a suite of ``basechange'' principles. I
  will then sketch how this abstract theory reduces the theorem to an eleme
 ntary Tate cohomology calculation by working with an equivariant topos. Th
 is is based on joint work with D. Kirstein and C. Kremer from arXiv:2405.1
 7641.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/78/
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