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SUMMARY:Emil V Prodan (Yeshiva University)
DTSTART:20200527T190000Z
DTEND:20200527T200000Z
DTSTAMP:20260420T052528Z
UID:NYC-NCG/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NYC-NCG/7/">
 Cyclic co-homology\, Fredholm modules\, Kasparov’s generalizations</a>\n
 by Emil V Prodan (Yeshiva University) as part of Noncommutative geometry i
 n NYC\n\n\nAbstract\nConsider an extended (Delone) point pattern in the d-
 dimensional Euclidean space such that each point hosts N degrees of freedo
 m. In many practical applications\, ranging from quantum materials to meta
 -materials\, one is interested in the collective dynamics of the degrees o
 f freedom hosted by the pattern. As we shall see\, the generators of any p
 attern-equivariant dynamics belong to a specific C*-algebra\, which in gen
 eral takes the form of a groupoid algebra and\, in more manageable cases\,
  of crossed products with discrete groups. The non-commutative geometry pr
 ogram for the aperiodic patterns consists in computing the C*-algebra\, it
 s K-theory and cyclic co-homology\, as well as establishing index theorems
  for the K-theory and cyclic co-homology pairings. In these seminars I wil
 l describe several interesting cases where this program has been carried a
 lmost entirely. I have a large number of numerical simulations\, which I w
 ill try to use throughout to exemplify the power of these methods.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/7/
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