Research

I'm interested in geometry, low dimensional topology, and geometric group theory. Much of my research revolves around questions about mapping class groups of both surfaces and graphs. Recently, I have been expanding my knowledge of heirarchically hyperbolic groups, Polish groups and learning more about descriptive set theory.

I consider myself an "extra low" dimensional topologist because some of my favorite spaces are graphs (1-dimensional CW complexes), and Stone spaces, which are (homeomorphic to) closed subsets of the Cantor set, and have zero topological dimension.

My dissertation is on the Lp metrics on Teichmüller space. I gave a short talk on the beginnings of this work at the Redbud Topology conference in Spring of 2021, the video of the talk is here.

As a master's student at Miami University I thought about Thompson's groups a lot, specifically the conjecture that Thompson's Group V is a universal coCF group. While advising a group of REU students as part of SUMSRI we proposed a potential counterexample to this conjecture.

Preprints and Publications

Coarse geometry of homeomorphism groups: Classifying countable Stone spaces. With G. Domat and R. Lyman. ( arXiv )

Constructing reducibly geometrically finite subgroups of the mapping class group. With T. Aougab, H. Bray, S. Dowdall, S. Maloni, B. Whitfield. To appear: Groups, Geometry, and Dynamics. ( arXiv )

Graphical models for topological groups: A case study on countable Stone spaces. With B. Branman, G. Domat, and R. Lyman. Bulletin of the LMS. ( Journal )

Complexity of Proper Homotopy Equivalence of Graphs. With J. Zomback. To appear: Proceedings of the AMS. ( arXiv )

Surfaces which are Proper Homotopy Equivalent to Graphs. With R. Dickman and S. Kwak. To appear: Michigan Mathematical Journal. ( arXiv )

The Lp Metrics on Teichmüller Space. Available on proquest.

Generating Sets and Algebraic Properties of Pure Mapping Class Groups of Infinite Graphs. With G. Domat and S. Kwak. Annales Henri Lebesgue. ( Journal )

The Automorphism Group of the Infinite-Rank Free Group is Coarsely Bounded. With G. Domat and S. Kwak. New York Journal of Math. ( Journal )

Coarse Geometry of Pure Mapping Class Groups of Infinite Graphs. With G. Domat and S. Kwak. Advances in Math. ( arXiv )

A New Construction of Subgroups of Big Mapping Class Groups. With C. Abbot, M. Loving, P. Patel, R. Skipper. New York Journal of Math. ( Journal )

Groups with Context-Free Co-Word Problem and Embeddings into Thompson's Group V. With R. Berns-Zieve, D. Fry, J. Gillings, H. Matthews. Appears in the LMS Lecture Note Series: Topological Methods in Group Theory ( arXiv )

Note: Open source publications are linked when available. Generally arXiv postings are up to date, but please contact me if you would like to view a published paper and do not have institutional access.