Marcin Sabok (McGill University)

Title: The Hrushovski property for hypertournaments and profinite topologies

Abstract: During the talk I will discuss a problem concerning extensions of partial isomorphisms of finite tournaments and its equivalent form, which is a problem about the pro-odd topology on the free group. The pro-odd topology is the refinement of the pro-finite topology where we take only the normal subgroups of odd index as the neighborhood basis of 1. The problem concerns a characterization of those finitely generated subgroups of the free group which are closed in the pro-odd topology. I will discuss a positive answer for cyclic subgroups and a negative answer for a generalized version of this question. Joint work with J. Huang, M. Pawliuk and D. Wise.