On the K-theoretic approach to density of states in quasi-crystals

Valerio Proietti  (ECNU)

14:00-15:00, April 12, 2019   Science Building A510

Abstract:

One approach to generalizing Bloch theory to non-periodic materials makes use of the standard tools of noncommutative topology, such as crossed product operator algebras, dual traces, and K-theory. With this language, I will describe a model based on independent electron approximation, where the main properties of the motion of delocalized electrons are studied through the electronic band structure and the associated values of the integrated density of states (roughly, the number of available energy levels per unit volume). We will discuss the mathematical problems around this framework and some techniques for their solution.

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