Slawomir Solecki
Ph.D. (1995) California Institute of Technology
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).
Selected Publications
Monoid actions and ultrafilter methods in Ramsey theory, to appear
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
Gδ 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 L0, 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