My research is in geometric group theory, metric geometry, and dynamical systems. Most recently I have been working to integrate tools from sub-Riemannian geometry for the study of finitely generated nilpotent groups, using horofunction boundaries to examine the dynamics of group actions and random walks. I am also interested in Teichmüller theory, mapping class groups, infinite-type surfaces, and translation surfaces.

For two months in 2019, I visited Javier Aramayona in Madrid as a GEAR graduate intern.

A 360º look at a sub-Finsler sphere in the Heisenberg group.

Research papers

• Sub-Finsler horofunction boundaries of the Heisenberg group, (with Sebastiano Nicolussi Golo). Analysis and Geometry in Metric Spaces, 2021. arXiv link
  • We give a complete analytic and geometric description of the horofunction boundary for polygonal sub-Finsler metrics – that is, those that arise as asymptotic cones of word metrics – on the Heisenberg group. We develop theory for the more general case of horofunction boundaries in homogeneous groups by connecting horofunctions to Pansu derivatives of the distance function.

• Stars at infinity in Teichmüller space, (with Moon Duchin). Geometriae Dedicata, 2021. arXiv link
  • We investigate a metric structure, called stars, developed by Anders Karlsson on the Thurston boundary of Teichmüller space. Along the way, we develop some metric geometric tools and explore stars in sup metrics.

Expository writing

• Here you can find a set of notes on nilpotent groups and their geometry, co-written with Moon Duchin.
• For my candidacy exam in December 2017, I studied curvature in complex hyperbolic space and its horofunction boundary. After the project, I wrote a set of notes introducing complex hyperbolic space, including an original exploration into its curvature. You can find those notes here.