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EducationPh.D. (2009) University of California at Los Angeles Research Area: descriptive set theory and mathematical logicMy primary research area is descriptive set theory. Of particular interest is the rich and blossoming study of the relative complexity of equivalence relations on Polish spaces. In addition to being set-theoretically interesting, questions in this area often involve ideas from other fields such as ergodic theory (e.g., investigating orbit equivalence relations of measure-preserving group actions) and combinatorics (e.g., understanding what sort of graph structures can be placed on equivalence classes). Selected PublicationsMeasurable chromatic and independence numbers for ergodic graphs and group actions (with A. S. Kechris), Groups, Geometry, and Dynamics (to appear). Canonizing relations on nonsmooth sets, in preparation. Descriptive set-theoretic dichotomy theorems and limits superior (with D. Lecomte and B. D. Miller), in preparation. Last modified: April 12, 2012 |