### Research Focus

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).

### Publications

Generic measure preserving transformations and the closed groups they generate, Invent. Math., to appear

- Monoid actions and ultrafilter methods in Ramsey theory, Forum of Mathematics, Sigma. 7 (2019), e2
- 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
- \(G_\delta\) 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
- 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

## In the news

- Math professors honored as AMS fellows
- Two Arts & Sciences Professors Elected to American Mathematical Society