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DTSTART;TZID=America/Los_Angeles:20231116T163000
DTEND;TZID=America/Los_Angeles:20231116T173000
DTSTAMP:20260514T170024
CREATED:20231113T045911Z
LAST-MODIFIED:20231113T045911Z
UID:3319-1700152200-1700155800@colleges.claremont.edu
SUMMARY:Continued fractions\, directed graphs\, and defining spectral triples on Effros-Shen AF algebras (Samantha Brooker\, Arizona State University)
DESCRIPTION:The Effros-Shen algebra corresponding to an irrational number $\theta$ can be described by an inductive sequence of direct sums of matrix algebras\, where the continued fraction expansion of $\theta$ encodes the dimensions of the summands\, and how the matrix algebras at the nth level fit into the summands at the (n+1)th level. In recent work\, Mitscher and Spielberg present an Effros-Shen algebra as the C*-algebra of a category of paths – a generalization of a directed graph – determined by the continued fraction expansion of \theta. With this approach\, the algebra is realized as the inductive limit of a sequence of infinite-dimensional\, rather than finite-dimensional\, subalgebras. Drawing on a construction by Christensen and Ivan\, we use this inductive limit structure to define a spectral triple\, trading the advantages of working with finite-dimensional approximants for the techniques provided by the category of paths\, pursuant to studying the algebras as quantum compact metric spaces. I will discuss categories of paths and their precursors\, graph C*-algebras\, the example of Mitscher and Spielberg\, and a bit about the spectral triple construction. This is joint work with Konrad Aguilar and Jack Spielberg.
URL:https://colleges.claremont.edu/ccms/event/continued-fractions-directed-graphs-and-defining-spectral-triples-on-effros-shen-af-algebras-samantha-brooker-arizona-state-university/
LOCATION:Estella 2141\, 610 N College Ave\, Claremont\, 91711\, United States
CATEGORIES:Analysis Seminar
ORGANIZER;CN="Asuman Aksoy":MAILTO:asuman.aksoy@claremontmckenna.edu
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