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For the most part, my research is motivated by mathematically interesting objects and phenomena arising in studying canonical topological spaces and dynamics of large groups (usually equipped with a metric separable, complete topology but lacking Haar measure). This research is informed by mathematical logic, in particular, by set theory and model theory and involves in essential ways combinatorics (Ramsey theory), probability theory (concentration of measure), and algebraic topology (fixed point theorems).
- Monoid actions and ultrafilter methods in Ramsey theory, to appear in Forum of Mathematics, Sigma.
- Unitary representations of the groups of measurable and continuous functions with values in the circle, J. Funct. Anal. 267 (2014), 3105--3124
- Abstract approach to finite Ramsey theory and a self-dual Ramsey theorem, Adv. Math. 248 (2013), 1156--1198
- GδGδ ideals of compact sets, J. Eur. Math. Soc., 13 (2011), 853--882
- The coset equivalence relation and topologies on subgroups, Amer. J. Math., 11 (2009), 571--605
- Extreme amenability of L0L0, a Ramsey theorem, and Levy groups, J. Funct. Anal., 255 (2008), 471--493, joint with I. Farah
- Projective Fraisse limits and the pseudo-arc, Trans. Amer. Math. Soc., 358 (2006), 3077--3096, joint with T. Irwin
- The structure of the space of composants of an indecomposable continuum, Adv. Math., 166 (2002), 149--192
- Analytic ideals and their applications, Ann. Pure Appl. Logic, 99 (1999), 51--72
- Decomposing Borel sets and functions and the structure of Baire class 1 functions, J. Amer. Math. Soc., 11 (1998), 521--550