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SUMMARY:Chris Kottke (New College of Florida)
DTSTART:20241018T150000Z
DTEND:20241018T161500Z
DTSTAMP:20260423T024751Z
UID:CIRGET/124
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CIRGET/124/"
 >Geometric analysis on quasi-fibered boundary (QFB) manifolds</a>\nby Chri
 s Kottke (New College of Florida) as part of CRM - Séminaire du CIRGET / 
 Géométrie et Topologie\n\nLecture held in PK-5115.\n\nAbstract\nThe know
 n complete non-compact hyperkahler manifolds include several families of m
 oduli spaces\, including the moduli spaces of SU(2) monopoles on R^3 and t
 he Hilbert schemes of points on C^2\, among others. Beyond dimension 4\, t
 he asymptotic geometries of these spaces are not uniform\, but exhibit sin
 gularities `at infinity’\, presenting a challenge for geometric analysis
 . I will report on a framework for geometric analysis for a broad class of
  `quasi-fibered boundary’ (QFB) metrics. The point of view is to conside
 r compactifications of these spaces as manifolds with corners\, which can 
 also be thought of as resolutions of certain stratified spaces. Through a 
 pseudodifferential parametrix construction for the Hodge de Rham operator 
 and an analysis relating weighted L2 cohomology with intersection cohomolo
 gy\, we prove a new case of Sen’s conjecture for the L2 cohomology of th
 e charge 3 monopole moduli space\, and of the Vafa-Witten conjecture for t
 he L2 cohomology of Hilbert schemes in all cases. This is joint work with 
 F. Rochon\n
LOCATION:https://researchseminars.org/talk/CIRGET/124/
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