Rooted in logic and descriptive set theory, my research lies in the nexus of ergodic theory, measured group theory, countable Borel equivalence relations, graph combinatorics, and geometric group theory.
Tree-like graphings, wallings, and median graphings of equivalence relations
(with Terence Tao) Banff International Research Station, Canada (July, 2015)
The Effros space of a σ-Polish space is standard Borel
UIUC (January, 2014)
Countable compact Hausdorff spaces are Polish
UCLA (March, 2013)
Segal's effective witness to measure-hyperfiniteness
Caltech (Fall, 2012)
Hjorth's proof of the embeddability of hyperfinite equivalence relations into E0
UCLA (Fall, 2010)
Contributions in others' works
Y. Moschovakis, Abstract Recursion and Intrinsic Complexity, to appear in the ASL Lecture Notes in Logic (2018)
Section 3B consists of the results of Part 3 of my Ph.D. thesis on complexity measures for recursive programs.
UCLA (Fall, 2009)
A. Kechris, The spaces of measure preserving equivalence relations and graphs, preprint (2017)
Sections 3, 6, 19 contain some of my results regarding the weak and strong topologies, the discontinuity of the map from actions to equivalence relations, and subtreeings of treeings of an equivalence relation.
Caltech (Spring, 2013)
M. Lupini, Polish groupoids and functorial complexity, Trans. of the Amer. Math. Soc., 369 (2017), no. 9, 6683–6723
Appendix consists of my proof of the Effros space of a σ-Polish space being standard Borel. [pdf]