Research

My area of research is descriptive set theory, more specifically the study of countable Borel equivalence relations and its interactions with other areas, especially ergodic theory and combinatorics.

Halloween 2023, dressed as myself

Halloween 2019, dressed as the scariest monster I could think of.

Publications and preprints

A backward ergodic theorem along trees and its consequences for free group actions [pdf, arXiv]

— with Anush Tserunyan

— Journal of European Math. Soc. (JEMS), to appear (2024+)

One-ended spanning trees and definable combinatorics [pdf, arXiv]

— with Matthew Bowen and Antoine Poulin

— Transactions of the American Math. Soc. , to appear (2024+)

A combinatorial proof of the pointwise ergodic theorem for actions of amenable groups along Tempelman Følner sequences [pdf, arXiv]

— with Jonathan Boretsky

— Bulletin Polish Acad. Sci. Math., published online (2024)

Colored unlinking [pdf, arXiv] (2019)

— with Natalie DuBois, Chris Eufemia, and Jeff Johannes

Papers with undergraduates

Uniform arithmetic in local rings via ultraproducts [pdf, arXiv] (2023)

— with Clay Adams, Francesca Cantor, Anese Gashi, Semir Mujevic, Sejin Park, and Austyn Simpson

On localization of tight closure in Line-S_4 Quartics [pdf, arXiv] (2022)

— with Levi Borevitz, Naima Nader, Theodore Sandstrom, Amelia Shapiro, and Austyn Simpson

— J. Pure and Appl. Algebra. 228 (2024), no. 9, Paper No. 107682

Characterization of saturated graphs related to pairs of disjoint matchings [pdf, arXiv] (2020)

— with Zhengda Mo, Sam Qunell, and Anush Tserunyan

— Illinois J. Math. 66(1): 59–77 (2022)

Pairs of disjoint matchings and related classes of graphs [pdf, arXiv] (2020)

— with Ali Guo, Kieran Kaempen, Zhengda Mo, Sam Qunell, Joe Rogge, Chao Song, and Anush Tserunyan

— Involve, a Journal of Mathematics 16-2 (2023), 249-264

Other writing

My understanding of "Mercuriale de groupes et de relations" by Damien Gaboriau [pdf] (2020)