## Departmental PhD Thesis Exam – Dana Bartosova

Everyone is welcome to attend. Refreshments will be served in the Math Lounge before the exam.

Friday, June 21, 2013
11:00 a.m.
BA 6183, 40 St George St.

Ph.D. Candidate: Dana Bartosova

Thesis Title: Topological dynamics in the language of near ultrafilters and automorphism groups of $\omega$-homogeneous structures

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In this thesis, we present a new viewpoint of the universal minimal flow in the language of near ultrafilters. We apply this viewpoint to generalize results of Kechris, Pestov and Todorcevic about a connection between groups of automorphisms of structures and structural Ramsey theory from countable to uncountable structures. This allows us to provide new examples of explicit descriptions of universal minimal flows as well as of extremely amenable groups. We identify new classes of finite structures satisfying the Ramsey property and apply the result to the computation of the universal minimal flow of the group of automorphisms of $\cal P (\omega_1)/$fin as well as of certain closed subgroups of groups of homeomorphisms of Cantor cubes. We furthermore apply our theory to groups of isometries of metric spaces and the problem of unique amenability of topological groups.

The theory combines tools from set theory, model theory, Ramsey theory, topological dynamics and ergodic theory, and homogeneous structures.

A soft copy of the thesis can be obtained by contacting dana.bartosova@mail.utoronto.ca