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SUMMARY:Higher order spectral shift and Callias operators [Oberseminar Glo
 bal Analysis and Operator Algebras]
DTSTART:20250603T121500Z
DTEND:20250603T131500Z
DTSTAMP:20260415T095000Z
UID:indico-event-400@math-events.uni-bonn.de
DESCRIPTION:Speakers: Oliver Fürst (Uni Bonn)\n\nThe spectral shift funct
 ion is a central object in mathematical scattering theory\, which was deve
 loped in the 50's by M. Krein. In the late 80's it reemerged in the contex
 t of index theory\, both as a replacement of Fredholm index and spectral f
 low for non-Fredholm operators. Due to the unstable nature of spectral shi
 ft\, it took until 2008 to show that the "Index=Spectral Flow"-theorem als
 o holds in this more general context\, which was done by A. Pushnitski. Si
 nce then\, many improvements have been developed in this essentially one-d
 imensional case.\n\nHowever\, the higher dimensional case\, which naturall
 y corresponds to Callias operators (Dirac operators with an operator-value
 d potential)\, was open until recently.\n\nIn this talk we show how the Fr
 edholm index and the top degree Chern character have to be regularized in 
 the higher dimensional case in terms of higher order spectral shift functi
 ons. These functions were conjectured in the 80's by Koplienko\, however t
 heir existence in all cases have only been shown in the relatively recent 
 past in 2013 by D. Potapov\, A. Skripka\, and F. Sukochev.\nWe present a n
 on-Fredholm version of the classical Callias index theorem and give some c
 oncrete examples\, in which the regularized index may assume any real numb
 er.\n \n\nhttps://math-events.uni-bonn.de/event/400/
LOCATION:Seminar room 1.008 (Mathezentrum)
URL:https://math-events.uni-bonn.de/event/400/
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