My research interests broadly center around low-dimensional topology and geometric group theory.
More recently I have been thinking about truncated braid groups, complex reflection groups, and some hyperbolic geometry and knot theory.
For short, I usually say that I enjoy "any math that comes with a good picture". At right is a random selection of pictures that have come from my own mathematical investigations, some about my own work and some about work of others.
Braid groups and Burnside groups. doi:10.48550/arXiv.2607.13316.
With T. Saffat, The 3-strand braid group with torsion. doi:10.48550/arXiv.2509.17900.
The Burau Representation and Shapes of Polyehdra. Algebraic and Geometric Topology. 24(5), 2787–2805. doi:10.2140/agt.2024.24.2787.
With A. Peterson, On Uniform Large-Scale Volume Growth for the Carnot-Caratheodory Metric on Unbounded Model Hypersurfaces in C^2, Involve, 11(1), 103–118, 2018. doi:10.2140/involve.2018.11.103.