Renormalization procedures for groupoids

Jeremy Hume (University of Glasgow)

Monday 22nd November, 2021 17:00-18:00 Room 311b

Abstract

Renormalization procedures for families of dynamical systems have been used to determine universal dynamical characteristics of analytic families of quadratic-like maps, to classify circle diffeomorphisms up to $C^{\infty}$ conjugation, to prove Keane’s conjecture for interval exchange mappings, and to provide a unique ergodicity criterion for the translation flow on a flat surface, known as Masur’s criterion.

Given the wide applicability of this renormalization theory, it is of interest to generalize it to the setting of groupoid bundles (families of groupoids), and their C*-algebraic counterparts, $C_{0}(X)$-algebras.

In these two talks, we will do so for bundles of étale groupoids. The end goal will be to present an analogue of Masur’s criterion for étale groupoids and use it to show that a variety of interesting groupoids have a unique invariant probability measure on their unit spaces.

In the first talk, we introduce renormalization procedures for families of dynamical systems for motivation, and the necessary pre-requisites to define renormalization procedures for groupoid bundles. This will include introducing groupoids themselves, groupoid bundles, and groupoid correspondences. We will conclude with the generalized definition of renormalization procedure and an example or two.

At room 311b  or virtually on zoom:
https://uofglasgow.zoom.us/j/94756156115?pwd=RXUzd3BrOEFxTk9zWWFHUUVycjRkZz09