My research is in hyperbolic geometry, Teichmüller theory and Morse theory. Recently I have been studying the topology of moduli of curves and their Deligne-Mumford compactification via Morse theory and hyperbolic geometry.
Papers:
(to be updated soon)
Morse theory on moduli of curves, submitted
Low Morse index for the systole function, submitted
The orthosystole of ideal polygons, with Samuel Dobchies and Maxime Fortier Bourque
Stability phenomena in Deligne-Mumford compactifications via Morse theory, submitted