Locally random groups

Abstract: Groups without non-trivial low dimensional representations, named quasi-random by Gowers, have recently found many applications in studying group theoretical problems of combinatorial nature. Loosely speaking, non-existence of such representations forces the product map on the group mapping $(a, b)$ to their product $ab$ to have a certain mixing behavior.

In this talk, after briefly recalling the notion of quasi randomness, I will discuss a generalisation of this concept to the class of compact groups. This property, called local randomness, is formulated in terms of unitary representations of the compact group $G$ and captures a similar mixing behavior at all scales. I will discuss a number of related results including a classification of locally random groups, a mixing inequality, and, if time allows, connection to spectral gap.

The talk is based on a joint work with Amir Mohammadi and Alireza Salehi Golsefidy.

dynamical systems

Audience: researchers in the topic

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Bremen Online Dynamics Seminar

Series comments: Talks are approx. 55 min plus discussion. Talks are not recorded.

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