Research

I'm interested in geometry, low dimensional topology, and geometric group theory. 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. I am also working on questions about Mapping Class Groups of surfaces of finite and infinite type, an analog of Out(F_n) for infinite, locally finite graphs, and free by cyclic groups. Recently, I have been expanding my knowledge of Polish groups and learning more about descriptive set theory.

I will often joke that I am an "extra low" dimensional topologist because some of my favorite spaces are graphs (1-dimensional CW complexes), and Stone spaces, which are closed subsets of the Cantor set, and have zero topological dimension.

While 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

Constructing reducibly geometrically finite subgroups of the mapping class group. With Tarik Aougab, Harrison Bray, Spencer Dowdall, Sara Maloni, Brandis Whitfield. ( arXiv )

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

Complexity of Proper Homotopy Equivalence of Graphs. With J. Zomback. ( arXiv )

Surfaces which are Proper Homotopy Equivalent to Graphs. With R. Dickman and S. Kwak. ( 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. To Appear: Annales Henri Lebesgue. ( arXiv )

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

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

Finding and Combining Indicable Subgroups of Big Mapping Class Groups. With C. Abbot, M. Loving, P. Patel, R. Skipper. ( arXiv )

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 )