Noncommutative geometry of topological phases of matterMPIM
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MPIM, Vivatsgasse, 7 - Lecture Hall
Max Planck Institute for Mathematics
Higher Differential Geometry Seminar
Jean Bellissard, in the 1980s, has realised that C*-algebras and their operator K-theory provide a unified framework to study topological phases of free fermionic systems. Among others, one of the most exciting achievement is an interpretation, in terms of noncommutative geometry (NCG), of the Kubo formula for the Integer Quantum Hall Effect. Over the past decade, ideas and methods from (topological) groupoids and coarse geometry have shed new light on how to understand topological phases of matter in a generic aperiodic system, and what "strong" topological phases should really mean. In this talk, I shall give a gentle introduction to the NCG ideas along the line, with an emphasis on the aperiodic setting. In particular, I shall explain how to construct interesting observable C*-algebras from a generic point pattern using groupoid methods.