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SUMMARY:Anton Yu. Savin (Peoples' Friendship University\, Moscow)
DTSTART:20200826T190000Z
DTEND:20200826T200000Z
DTSTAMP:20260420T053037Z
UID:NYC-NCG/19
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NYC-NCG/19/"
 >A local index formula for metaplectic operators</a>\nby Anton Yu. Savin (
 Peoples' Friendship University\, Moscow) as part of Noncommutative geometr
 y in NYC\n\n\nAbstract\nLet A be the algebra of unitary operators acting i
 n $H=L_2(R^n)$ and generated by translations\, orthogonal transformations\
 , products with exponentials $e^{ikx}$\nand fractional Fourier transforms.
  Equivalently\, A is the algebra generated by quantizations of isometric a
 ffine canonical transformations in $T^*R^n$. We show that the well-known i
 ndex one operator in $R^n$ (which is obtained from the creation and annihi
 lation operators\, see Higson-Kasparov-Trout 1998) denoted by D defines a 
 spectral triple (A\,H\,D) in the sense of Connes. Our main result is an ex
 plicit formula for the Connes--Moscovici residue cocycle for this spectral
  triple.  For the subalgebra in A generated by translations and exponentia
 ls\, this gives a local index formula for noncommutative tori. \nThis is j
 oint work with Elmar Schrohe (Hannover)\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/19/
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