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SUMMARY:Emil V Prodan (Yeshiva University)
DTSTART:20200603T190000Z
DTEND:20200603T200000Z
DTSTAMP:20260420T052656Z
UID:NYC-NCG/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NYC-NCG/5/">
 Index theorems in KK-theory</a>\nby Emil V Prodan (Yeshiva University) as 
 part of Noncommutative geometry in NYC\n\n\nAbstract\nConsider an extended
  (Delone) point pattern in the d-dimensional Euclidean space such that eac
 h point hosts N degrees of freedom. In many practical applications\, rangi
 ng from quantum materials to meta-materials\, one is interested in the col
 lective dynamics of the degrees of freedom hosted by the pattern. As we sh
 all see\, the generators of any pattern-equivariant dynamics belong to a s
 pecific C*-algebra\, which in general takes the form of a groupoid algebra
  and\, in more manageable cases\, of crossed products with discrete groups
 . The non-commutative geometry program for the aperiodic patterns consists
  in computing the C*-algebra\, its K-theory and cyclic co-homology\, as we
 ll as establishing index theorems for the K-theory and cyclic co-homology 
 pairings. In these seminars I will describe several interesting cases wher
 e this program has been carried almost entirely. I have a large number of 
 numerical simulations\, which I will try to use throughout to exemplify th
 e power of these methods.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/5/
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