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Set theory, mathematical logic, and set theoretic topology.
My primary area of research is set theory, infinite combinatorics, and their applications to other fields of mathematics such as topology, functional analysis, and algebra. Recently I have focused on improving our understanding of groups closely related to the group of piecewise linear homeomorphisms of the unit interval.
- A nonamenable finitely presented group of piecewise projective homeomorphisms (with Yash Lodha), Groups Geom. Dyn. 10 (2016), no. 1, 177–200.
- Fast growth in the Følner function for Thompson's group F. Groups, Geometry, and Dynamics 7 (2013), no. 3, pp. 633–651.
- Forcing axioms and the continuum hypothesis (with David Aspero and Paul Larson), Acta Mathematica. 210 (2013), no. 1, pp. 1-29.
- A Boolean action of C(M,U(1))C(M,U(1)) without a spatial model and a re-examination of the Cameron-Martin Theorem (Solecki, Slawomir), J. Funct. Anal. 263 (2012), no. 10, pp. 3224–3234.
- The proper forcing axiom. Proceedings of the International Congress of Mathematicians, Volume II, 3–29, Hindustan Book Agency, New Delhi, 2010.
- A solution to the L space problem, Journal of the American Mathematical Society 19 no. 3 (2006), pp. 717–736.
- A five element basis for the uncountable linear orders, Annals of Mathematics (2) 163 no. 2 (2006), pp. 669–688.