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SUMMARY:A KK-theoretic perspective on the spectral localiser [Oberseminar 
 Global Analysis and Operator Algebras]
DTSTART:20261103T131500Z
DTEND:20261103T141500Z
DTSTAMP:20261030T013100Z
UID:indico-event-1700@math-events.uni-bonn.de
DESCRIPTION:Speakers: Koen van den Dungen (Mathematical Institute)\n\nThe 
 index pairing between K-theory and K-homology is usually expressed as a Fr
 edholm index on an infinite-dimensional Hilbert space. The construction of
  the spectral localiser (due to Loring and Schulz-Baldes) allows to reduce
  such an index pairing to the computation of a finite matrix\, thus making
  the index pairing accessible to numerical calculations. In this talk\, I
  will describe a new perspective on the spectral localiser in the context 
 of KK-theory. The KK-theoretic approach provides a spectral flow expressio
 n for the even or odd index pairing in terms of the "infinite volume" spec
 tral localiser\, and has the main advantage that the construction of the s
 pectral localiser becomes immediately apparent from the computation of the
  index pairing via a Kasparov product. Next\, in a second step of "spectr
 al truncation" (closely following Loring and Schulz-Baldes)\, I will expla
 in how this spectral flow expression can be computed in terms of the signa
 ture of the "finite volume" spectral localiser. \n\nhttps://math-events.u
 ni-bonn.de/event/1700/
LOCATION:Endenicher Allee 60/1.008 (Mathezentrum) (Mathezentrum)
URL:https://math-events.uni-bonn.de/event/1700/
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