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+)
Discrete Mathematics, vol. 308 (2008), no. 23, pp. 5823–5828
Supervised undergraduate research
Alexandra (Sasha) Bell and Owen Rodgers, A modern exposition of Kakutani’s criterion for equivalence of product measures, McGill Undergraduate Research Project, Summer 2023 [pdf]
Thomas Buffard, Gabriel Levrel, and Sam Mayo, Borel Determinacy: a streamlined proof, McGill Undergraduate Research Project, Fall 2021 [pdf]
Ph.D. Thesis
Finite generators for countable group actions; Finite index pairs of equivalence relations; Complexity measures for recursive programs [pdf, ProQuest]
UCLA (May, 2013)
Other writing
The following are some things I've written that are either partially published or not (currently) intended for publication.
A descriptive set theorist's proof of the pointwise ergodic theorem [arXiv]
(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]