For a summary of my research, here is an old research statement (from 2019). At some point, I'll write a statement for a broader audience, but that's a work in progress. A complete list of publication can be found on my CV (updated June 2023)

 My main research focus is geometric analysis, which uses techniques from PDEs to study problems in geometry. Here are some topics which I find interesting.

  • Geometric flows (e.g., Ricci flow, curve-shortening flow)
  • Spectral geometry
  • Optimal transport
  • Information geometry
  • Geometric probability

Selected research and exposition