Spectral truncations and convergence of compact quantum metric spaces

Malte Leimbach (Radboud University)

Thursday 14th November 16:00-17:00 Maths 311B

Abstract

A fundamental principle of noncommutative geometry is to encode geometric information by spectral data, formalised in the notion of spectral triples. In physical practice there are, however, always obstructions on the availability of such data, and one might be led to considering truncated versions of spectral triples instead. In this talk we will take a closer look at this formalism and explore it within the framework of compact quantum metric spaces. In particular, we will discuss how one might appropriately approximate spectral triples by their truncated versions. As concrete examples we will consider spectral truncations of tori and Peter--Weyl truncations of compact quantum groups.

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