## Linear Analysis Seminar

**Date:** March 9, 2018

**Time:** 4:00PM - 5:00PM

**Location:** BLOC 220

**Speaker:** Alexandru Chirvasitu, University at Buffalo

**Title:** *Most metric spaces are very asymmetric*

**Abstract:** Compact quantum groups are the non-commutative geometer's version of a compact group, and their actions on geometric or algebraic objects capture extended notions of symmetry, generalizing the concept of a structure-preserving automorphism. The talk will explain what it means for a compact quantum group action on a compact metric measure space to preserve the entirety of the structure (metric as well as measure-theoretic). The main result is then a reflection of the general intuition that most objects are not very symmetric: upon topologizing the set of isomorphism classes of metric measure spaces it transpires that ``the majority'' admit no symmetry, even when relaxing the notion of symmetry to allow for its quantum counterpart. (partly joint w/ Martino Lupini, Laura Mancinska and David Roberson)