# Andy Zucker: Maximal equivariant compactifications of categorical metric structures

Mathematical logic seminar – Mar 27 2018
Time:     3:30pm – 4:30 pm

Room:     Wean Hall 8220

Speaker:         Andy Zucker
Department of Mathematical Sciences
CMU

Title:     Maximal equivariant compactifications of categorical metric structures

Abstract:

Any completely regular space embeds into a compact space. But suppose G is a topological group and X is a completely regular G-space. There is a largest G-map αX: X → Y where Y is compact and αX has dense image, but αX need not be an embedding. Recently, Pestov has constructed an example of a topological group G and non-trivial flow X for which αX is the map to a singleton.

In this talk, we consider automorphism groups of categorical metric structures, which include the Urysohn sphere, the unit sphere of the Banach lattice Lp, and the unit sphere of the Hilbert space L2. We show that if G is the group of automorphisms of a categorical metric structure X, then αX is the embedding of X into the space of 1-types over X.

(Joint work with Itai Ben Yaacov)