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.
Preprints
Tree-like graphings, wallings, and median graphings of equivalence relations
[arXiv] (2023+)
Ergodic Theory and Dynamical Systems: Proceedings of the Workshops University of North Carolina at Chapel Hill 2021, edited by Idris Assani, Berlin, Boston: De Gruyter (2024), pp. 99–116.
Pairs of disjoint matchings and related classes of graphs [arXiv, DOI]
▻with H. Guo, K. Kaempen, Z. Mo, S. Qunell, J. Rogge, C. Song, J. Zomback
Involve, a Journal of Mathematics 16-2 (2023), 249–264
Mixing and double recurrence in probability groups
[arXiv, DOI]
Fundamenta Mathematicae 260 (2023), 77–98
Pointwise ergodic theorem for locally countable quasi-pmp graphs
[arXiv, DOI]
Journal of Modern Dynamics, 18 (2022), 609–655
Characterization of saturated graphs related to pairs of disjoint matchings [arXiv, DOI]
(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]