Research

My research is in hyperbolic geometry, Teichmüller theory, geometric topology, Morse theory, extremal problems, and randomness problems. Recently I have been studying the topology of moduli of curves and their Deligne-Mumford compactification from a Morse and Teichmüller theoretic perspective.

Papers:

1. Morse theory on moduli of curves, submitted

2. Index gap of the systole function, submitted

3. The orthosystole of ideal polygons, with Samuel Dobchies and Maxime Fortier Bourque, draft

4. Stability phenomena in Deligne–Mumford compactifications via Morse theory, submitted

5. Shortest k-geodesics on hyperbolic surfaces, submitted

6. (In preparation) X-collar lemma and the Weil–Petersson pairing of length gradients