Slawomir Solecki
Professor
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), 31053124
 Abstract approach to finite Ramsey theory and a selfdual Ramsey theorem, Adv. Math. 248 (2013), 11561198
 \(G_\delta\) ideals of compact sets, J. Eur. Math. Soc., 13 (2011), 853882
 The coset equivalence relation and topologies on subgroups, Amer. J. Math., 11 (2009), 571605
 Projective Fraisse limits and the pseudoarc, Trans. Amer. Math. Soc., 358 (2006), 30773096, joint with T. Irwin
 The structure of the space of composants of an indecomposable continuum, Adv. Math., 166 (2002), 149192
 Analytic ideals and their applications, Ann. Pure Appl. Logic, 99 (1999), 5172
 Decomposing Borel sets and functions and the structure of Baire class 1 functions, J. Amer. Math. Soc., 11 (1998), 521550