## 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)