University of Utah, USA
Research Areas:
Geometric and Combinatorial Group theory
Short Research Summary:
I work in geometric group theory which means I study groups via the spaces on which they act. Most of the groups that arise in my research come from automorphisms of rooted trees or almost-automorphisms of rooted trees, meaning they look like an automorphism outside of some finite subset of the tree. These groups often arise in dynamics and can be thought of as living in the group of homeomorphisms of the cantor set. They also have connections to big mapping class groups, which is the group of orientation preserving homeomorphisms of a surface which pointwise fix the boundary, taken up to isotopy where the fundamental group of the surface is not finitely generated. I like to study the algebraic, geometric, and topological properties of these groups. The most well-known groups which show up in my research are Grigorchuk's group and Thompson's group's F, T and V.
Introductory book/lecture notes:
a) Clara Loeh: Geometric Group Theory, An Introduction
b) Cannon, Floyd, and Parry: Introductory Notes on Richard Thompson's groups
c) Skipper: Groups acting on rooted trees, Groups acting on fractals, hyperbolicity and self-similarity, Panoramas et Synth ́eses 63 (2025) (this can also be found on my website and will be the basis the notes for my minicourse, so I don't know if you want to share it now or wait until the minicourse).
Mentee Assessment:
The assessment will be done as a catch-up session during Topology and Algebras Workshop 2026.