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SUMMARY:Index theory for unbounded Fredholm operators [Oberseminar Global 
 Analysis and Operator Algebras]
DTSTART:20251125T131500Z
DTEND:20251125T144500Z
DTSTAMP:20260314T235600Z
UID:indico-event-933@math-events.uni-bonn.de
DESCRIPTION:Speakers: Marina Prokhorova (MPIM Bonn / University of Haifa\,
  Technion – Israel Institute of Technology)\n\nAs was shown in classical
  works of Atiyah\, Jänich\, and Singer\, the space of bounded Fredholm op
 erators represents even K-theory\, while its subspace consisting of self-a
 djoint operators (more precisely\, its non-trivial connected component) re
 presents odd K-theory. The index theory of elliptic differential operators
  on closed manifolds is based on these classical results.However\, in some
  situations\, e.g. for elliptic operators on manifolds with boundary\, one
  needs to deal with families of unbounded operators. My talk is devoted to
  an index theory of such families. I will explain how relevant spaces of u
 nbounded operators are related to classical spaces of bounded Fredholm ope
 rators and show that natural maps between them are homotopy equivalences. 
 In addition\, I will answer a question raised in 2001 by Booss-Bavnbek\, L
 esch\, and Phillips.\nThe talk is based on my preprint arXiv:2110.14359 . 
 If time permits\, I will also mention a related result of arXiv:2202.03337
  .\n\nhttps://math-events.uni-bonn.de/event/933/
LOCATION:Endenicher Allee 60/1-008 (Mathezentrum)
URL:https://math-events.uni-bonn.de/event/933/
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