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SUMMARY:Index theory for unbounded Fredholm operators II [Oberseminar Glob
 al Analysis and Operator Algebras]
DTSTART:20251209T131500Z
DTEND:20251209T144500Z
DTSTAMP:20260314T233900Z
UID:indico-event-985@math-events.uni-bonn.de
DESCRIPTION:Speakers: Marina Prokhorova (MPIM\, University of Haifa & Tech
 nion)\n\nIn continuation of my previous talk two weeks ago\, I will show o
 ther approaches to\nindex theory for families of unbounded Fredholm operat
 ors in a Hilbert space. I will\nstart by recalling basic notions for those
  who were not present at the first talk.\nThen I will show how one can mod
 ify a graph continuous family by an appropriate\n“change of coordinates
 ”\, giving rise to a norm continuous family of Fredholm\noperators. For 
 self-adjoint operators\, the situation is more complicated\; I will\ndescr
 ibe arising obstructions and show that such an “improving of topology”
  can\nstill be achieved in most important cases. In particular\, these res
 ults explain why\na proof of existence of spectral sections by Melrose and
  Piazza is working for\nfibrations. The talk is based on my preprint arXiv
 :2202.03337. I will also briefly\npresent a recent approach of N.V. Ivanov
  to index theory of families\n(arXiv:2111.15081)\, which works even under 
 much weaker continuity assumptions.\n\n\nhttps://math-events.uni-bonn.de/e
 vent/985/
LOCATION:Endenicher Allee 60/1-008 (Mathezentrum)
URL:https://math-events.uni-bonn.de/event/985/
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