19/July/2013, 13:30-15:00

Fields Institute, Room 210

Speaker: Todor Tsankov

Title: On some generalizations of de Finetti’s theorem

Abstract:

A permutation group G acting on a countable set M is called

oligomorphic if the action of G on M^n has only finitely many orbits

for each n. Those groups are well known to model-theorists as

automorphism groups of omega-categorical structures. In this talk, I

will consider the question of classifying all probability measures on

[0, 1]^M invariant under the natural action of the group G. A number

of classical results in probability theory due to de Finetti,

Ryll-Nardzewski, Aldous, Hoover, Kallenberg, and others fit nicely

into this framework. I will describe a couple of new results in the

same spirit and a possible approach to carry out the classification in

general.