I am broadly interested in Teichmüller theory (higher rank and classical) and the surrounding mathematics. I have recently been working on questions on the Thurston-Klein geometry of Hitchin representations in PSL(n,R) and on Thurston's asymmetric metric on Teichmüller space.

Here is a list of my papers since the start of graduate school:

Research:

• On Foliations in PSL(4,R) Teichmüller Theory (preprint).

• Metrics on Hitchin components from Hölder distortion (2024) (arxiv).

• Leaves of foliated projective structures, Accepted for publication in Advances in Mathematics, (arxiv, journal).

• (with Tamunonye Cheetham-West) Characterizing candidates for Cannon's Conjecture from geometric measure theory, Bulletin LMS, 2023 (arXiv, journal)

• Higher degree complex structures. Oberwolfach Reports 47 (2022). 44-47.

• Canonical maps from spaces of higher complex structures to Hitchin components (2022, arXiv).

In Summer 2018, I was a participant in an (NSF funded) international research experience in Uzbekistan, which led to the following: 

Undergraduate Research:

• An application of Abel's method to the inverse Radon transform (with S. Alimov, J. David, J. Sherman, 2019, arXiv)

• A boundary-value problem for the 3-D fractional wave equation with singularity (with J. David, J. Sherman, 2018, arXiv)

I have given the following invited talks:

• University of Chicago Geometric Analysis seminar (2024)

• Washington University of St. Louis Geometry-Topology seminar (2024)

• SE AMS sectional at Tallahassee special session in geometry and topology (2024)

• Rice University geometry and topology seminar (2023)

• University of Luxembourg geometry and topology seminar (2023)

• Université de Strasbourg geometry and topology seminar (2023) 

• Universität Heidelberg geometry and topology seminar (2023)

• Workshop: Metrics on Higher Teichmüller spaces (2023, 150-minute expository talk on the Bridgeman-Taylor metric on Quasi-Fuchsian space)

• SE AMS Sectional, Special Session in Geometric Group Theory (2023)

• Georgia Tech topology seminar (2023)

• Université Côte d'Azur geometry seminar (2022) 

• University of Luxembourg geometry and topology seminar (Fall 2022)

• University of Pavia geometry Seminar (2022)

• Arbeitsgemeinschaft on Higher Teichmüller Theory (Oberwolfach) (2022, 75-minute expository talk on higher complex structures)

• Geometric Structures NextGen Seminar (2022)

• Wesleyan college graduate student seminar (2022)

• Universität Heidelberg geometry and topology seminar (2022)

• University of Luxembourg geometry and topology seminar (Summer 2022)

• Geometry and topology graduate and postdoc seminar (GT GAPS) (2022)

• UMass Amherst geometry and topology seminar (2022)

• Chern Math Institute at Nankai University geometry and topology seminar (2022)