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CREATED:20190709T131328Z
DESCRIPTION:Speaker: Claude Schochet\, Technion\nTitle: \;Cohomology an
d K-Theory for Tilings\nAbstract: \;An aperiodic tiling of R^d has a h
ull\, which typically is a compact foliated space X. The hull comes equipp
ed with an invariant transverse measure\, corresponding to a Z^d-invariant
measure on a totally disconnected transversal N. Mathematical physicists
attach two types of invariants to this situation. On the one hand\, the in
variant transverse measure gives rise to a real-valued map on H^d(X\; R) (
Cech cohomology) which corresponds to the diffraction pattern aspect of ti
lings. \; On the other hand. it also gives rise to a real-valued map o
n K_0(C^*G(X))\, the topological K-theory of the C^*-algebra of the holono
my groupoid of the tiling\, which corresponds to the spectral (of Hamilton
ians defined on such tilings) aspect of tilings. \; We use the Index T
heorem for foliated spaces to prove that under some general assumptions th
at these points of view are equivalent. This is joint work with Eric Akker
mans (physics\, the Technion) and Jonathan Rosenberg (math\, U. Maryland).
DTSTART:20190910T140000
DTEND:20190910T150000
LOCATION:FacultyAdministration
SUMMARY:Mathematics Topology Seminar - Claude Schochet
TRANSP:OPAQUE
URL:https://events.wayne.edu/research-events/2019/09/10/mathematics-topolog
y-seminar-claude-schochet-82563/
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