K-theory in solid-state physics: modelling and computationMPIM
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MPIM, Vivatsgasse, 7 - Lecture Hall
Max Planck Institute for Mathematics
Commutative algebras can be viewed as certain function algebras on geometric spaces. This perspective motivates the philosophy of noncommutative geometry, which studies noncommutative algebras as if they are functions on noncommutative spaces.
In the 1980s, Jean Bellissard developed a surprisingly elegant and powerful framework, allowing for modelling quantum solid-state systems as noncommutative spaces. Their algebraic topology --- that is, topological K-theory --- encodes rich information that can be exactly measured in a physical experiment.
Over the past decade, new ideas and methods have emerged in this area, surrounding the following two questions:
1. How to effectively model a solid-state system, in a way that captures only the physically relevant topological information?
2. How to efficiently compute the numerical invariants of a model system, particularly when only partial information is available?
The goal of my talk is to provide an overview of the K-theoretic approach to solid-state physics, and discuss some ideas and results related to these questions.