Emmy-Noether-Seminar: Spectral measures in tensor categories and applications

Spectral measures in tensor categories and applications

Emmanuel Kowalski (Zürich)

Abstract: (joint work with A. Forey and J. Fresán)

Given an object M of a tensor category, and a suitable numerical invariant (such as the multiplicity of the unit object, in the semisimple case), a spectral measure for M is a positive measure, if it exists, whose moments give the values of the invariant on the tensor powers of M.

We will discuss some of the motivation behind this notion (coming from number theory), as well as examples, focusing on the case of tensor envelope categories, where spectral measures lead to new proofs of old results on fixed-point statistics in certain situations. We will also mention open questions and speculations.