Kurt Gödel Research Center

2012 seminar talk: The Poulsen simplex as a Fraisse limit

Talk held by Asger Törnquist (University of Copenhagen, Denmark) at the KGRC seminar on 2012-10-18.

Abstract

A Choquet simplex is an infinite dimensional generalization of the classical notion of a simplex (a polytope where every point is uniquely the convex combination of extremal points). Choquet asked in the 1950's if there is a metrizable Choquet simplex where the extremal boundary is dense in the simplex. This question was answered in the affirmative by Ebbe Thue Poulsen in a 1961 paper. Later, in 1978, it was shown that by Lindenstrauss, Olsen and Sternfeld that Poulsen's simplex is unique (with the prescribed properties) up to affine continuous isomorphism, and, moreover, that it is a highly homogeneous object.

In this talk, I will discuss how the Poulsen simplex, P, can be constructed as a Fraisse limit. I will also discuss some vexing questions related to the automorphism group of P.

This is joint work with Clinton Conley (formerly of the KGRC, now at Cornell).

Please note: The talk has been rescheduled to Thursday, October 18, 10:30am.