My research is mainly in descriptive set theory and its connections with ergodic theory, measured group theory, geometric group theory, and combinatorics.
Publications and preprints
The structure of hyperfinite equivalence relations in a quasi-pmp acyclic graph (2018)
(with Terence Tao) Banff International Research Station, Canada (July, 2015)
The Effros space of a σ-Polish space is standard Borel
[pdf]
UIUC (January, 2014)
Countable compact Hausdorff spaces are Polish
[pdf]
UCLA (March, 2013)
Segal's effective witness to measure-hyperfiniteness
[pdf]
Caltech (Fall, 2012)
Hjorth's proof of the embeddability of hyperfinite equivalence relations into E_{0}
[pdf]
UCLA (Fall, 2010)
Contributions in others' works
Y. Moschovakis, Abstract Recursion and Intrinsic Complexity, to appear in the ASL Lecture Notes in Logic (2018)
[pdf]
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)
[pdf]
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
[arXiv]
Appendix consists of my proof of the Effros space of a σ-Polish space being standard Borel. [pdf]