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 Gspace. There is a largest Gmap α_{X}: X → Y where Y is compact and α_{X} has dense image, but α_{X} need not be an embedding. Recently, Pestov has constructed an example of a topological group G and nontrivial flow X for which α_{X} 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 L_{p}, and the unit sphere of the Hilbert space L_{2}. We show that if G is the group of automorphisms of a categorical metric structure X, then α_{X} is the embedding of X into the space of 1types over X. (Joint work with Itai Ben Yaacov) 