Publications

Lacunary sets and actions of tsi groups. Submitted.
Recurrence and the existence of invariant measures. With Manuel Inselmann. Submitted.
Edge sliding and transverse hyperfinite decompositions. With Anush Tserunyan. Submitted.
On the existence of cocycle-invariant Borel probability measures. Submitted.
Bases for functions beyond the first Baire class. With Raphaël Carroy. Submitted.
Open graphs, Hurewicz-style dichotomies, and the Jayne-Rogers theorem. With Raphaël Carroy. Submitted.
Incomparable actions of free groups. With Clinton Conley. To appear in Ergodic theory and dynamical systems.
Sigma-continuity with closed witnesses. With Raphaël Carroy. Fundamenta Mathematicae, 29-42, 239, 2017.
Measurable perfect matchings for acyclic locally countable Borel graphs. With Clinton Conley. Journal of Symbolic Logic, 258-271, 82 (1), 2017.
Dichotomy theorems for families of non-cofinal essential complexity. With John Clemens and Dominique Lecomte. Advances in Mathematics, 285-299, 304, 2017.
Orthogonal measures and strong ergodicity. With Clinton Conley. Israel Journal of Mathematics, 83-89, 218 (1), 2017.
Measure reducibility of countable Borel equivalence relations. With Clinton Conley. Annals of Mathematics, 347-402, 185 (2), 2017.
A bound on measurable chromatic numbers of locally finite Borel graphs. With Clinton Conley. Mathematical Research Letters, 1633-1644, 23 (6), 2016.
The smooth ideal. With Clinton Conley and John Clemens. Proceedings of the London Mathematical Society, 57-80, 112 (1), 2016.
An embedding theorem of E0 with model theoretic applications. With Itay Kaplan. Journal of Mathematical Logic, 1450010, 14 (2), 2014.
The Borel cardinality of Lascar strong types. With Itay Kaplan and Pierre Simon. Journal of the London Mathematical Society, 609-630, 90 (2), 2014.
Essential countability of treeable equivalence relations. With John Clemens and Dominique Lecomte. Advances in Mathematics, 1-31, 265, 2014.
An antibasis result for graphs of infinite Borel chromatic number. With Clinton Conley. Proceedings of the American Mathematical Society, 2123-2133, 142 (6), 2014.
Stationary probability measures and topological realizations. With Clinton Conley and Alexander Kechris. Israel Journal of Mathematics, 333-345, 198 (1), 2013.
Incomparable treeable equivalence relations. Journal of Mathematical Logic, 121-162, 12 (1), 2012.
The graph-theoretic approach to descriptive set theory. Bulletin of Symbolic Logic, 554-575, 18 (4), 2012.
Definability of small puncture sets. With Andres Caicedo, John Clemens, and Clinton Conley. Fundamenta Mathematicae, 39-51, 215 (1), 2011.
Dichotomy theorems for countably infinite dimensional analytic hypergraphs. Annals of Pure and Applied Logic, 561-565, 162 (7), 2011.
A classical proof of the Kanovei-Zapletal canonization. Contemporary Mathematics, 281-285, 533, American Mathematical Society, 2011.
Descriptive Kakutani equivalence. With Christian Rosendal. Journal of the European Mathematical Society, 179-219, 12 (1), 2010.
Ends of graphed equivalence relations, II. With Greg Hjorth. Israel Journal of Mathematics, 393-415, 169, 2009.
Ends of graphed equivalence relations, I. Israel Journal of Mathematics, 375-392, 169, 2009.
Basis theorems for non-potentially closed sets and graphs of uncountable Borel chromatic number. With Dominique Lecomte. Journal of Mathematical Logic, 121-162, 8 (2), 2008.
Measurable chromatic numbers. Journal of Symbolic Logic, 1139-1157, 73 (4), 2008.
The existence of quasi-invariant measures of a given cocycle, II: Probability measures. Ergodic Theory and Dynamical Systems, 1615-1633, 28 (5), 2008.
The existence of quasi-invariant measures of a given cocycle, I: Atomless, ergodic sigma-finite measures. Ergodic Theory and Dynamical Systems, 1599-1613, 28 (5), 2008.
Means on equivalence relations. With Alexander Kechris. Israel Journal of Mathematics, 241-263, 163, 2008.
Coordinatewise decomposition of group-valued Borel functions. Fundamenta Mathematicae, 119-126, 196 (2), 2007.
Isomorphism of Borel full groups. With Christian Rosendal. Proceedings of the American Mathematical Society, 517-522, 135 (2), 2007.
Coordinatewise decomposition, Borel cohomology, and invariant measures. Fundamenta Mathematicae, 81-94, 191 (1), 2006.
Topics in orbit equivalence. With Alexander Kechris. Lecture Notes in Mathematics, 1852, Springer, 2004.