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DTSTAMP:20261012T111800Z
SUMMARY:GATP Seminar – Geordie Williamson (Sydney): Intersection homology
  over rings
DESCRIPTION:Intersection (co)homology is a beautiful invariant of singular 
 spaces\, e.g. singular complex algebraic varieties. Over the rationals it 
 satisfies a raft of strong properties (e.g. Poincaré duality\, hard Lefsc
 hetz\, pure Hodge structure\,…) which still seem like a miracle. In thei
 r paper introducing these groups\, Goresky and MacPherson point out that (
 unlike the integral cohomology of smooth manifolds) it fails to satisfy Po
 incaré duality over the integers. Subsequent sheaf theoretic approaches h
 ave clarified the situation\, and in fact one can prove that there is no r
 easonable theory over the integers which satisfies Poincaré duality. I wi
 ll discuss intersection cohomology\, given several simple examples that il
 lustrate the theory. Then I will discuss work in progress with F. Klein an
 d T. Fell where we introduce self-dual theory over certain p-adic rings. I
 nterestingly\, a self-dual theory exists if one is allowed to add enough r
 oots of p. We don’t quite know what to make of this\, but maybe someone 
 in the audience does…
URL:https://www.imperial.ac.uk/events/214877/gatp-seminar-geordie-williamso
 n-sydney-intersection-homology-over-rings/
DTSTART;TZID=Europe/London:20261020T110000
DTEND;TZID=Europe/London:20261020T123000
LOCATION:Huxley 658\, Huxley Building\, South Kensington Campus\, Imperial 
 College London\, London\, SW7 2AZ\, United Kingdom
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