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SUMMARY:Emil V Prodan (Yeshiva University)
DTSTART:20200520T190000Z
DTEND:20200520T200000Z
DTSTAMP:20260420T052742Z
UID:NYC-NCG/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NYC-NCG/6/">
 The C*-algebra of equivariant Hamiltonians over point patterns</a>\nby Emi
 l V Prodan (Yeshiva University) as part of Noncommutative geometry in NYC\
 n\n\nAbstract\nConsider an extended (Delone) point pattern in the d-dimens
 ional Euclidean space such that each point hosts N degrees of freedom. In 
 many practical applications\, ranging from quantum materials to meta-mater
 ials\, one is interested in the collective dynamics of the degrees of free
 dom hosted by the pattern. As we shall see\, the generators of any pattern
 -equivariant dynamics belong to a specific C*-algebra\, which in general t
 akes the form of a groupoid algebra and\, in more manageable cases\, of cr
 ossed products with discrete groups. The non-commutative geometry program 
 for the aperiodic patterns consists in computing the C*-algebra\, its K-th
 eory and cyclic co-homology\, as well as establishing index theorems for t
 he K-theory and cyclic co-homology pairings. In these seminars I will desc
 ribe several interesting cases where this program has been carried almost 
 entirely. I have a large number of numerical simulations\, which I will tr
 y to use throughout to exemplify the power of these methods.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/6/
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