I’m broadly interested in topics at the intersection of number theory, representation theory and algebraic geometry. These days, I am thinking most about:

  • regularizing relative trace formulas (RTFs)
  • stabilizing relative trace formulas, and relative endoscopy
  • the internal structure of distinguished local packets

Publications and Preprints

  1. The Relative Trace Formula for Galois Periods (2025) Last updated: Nov. 2025 (arXiv).

    This work has two components: First, I introduce truncated geometric and spectral RTF distributions for a broad class of Galois symmetric pairs (including all Galois symmetric pairs arising from split connected reductive groups) and formulate a precise coarse RTF identity. Next, I specialize to the Galois symmetric pair \(\mathrm{SL}_{2, F} \subset \mathrm{Res}_{E/F} \mathrm{SL}_{2, E}\), where I prove convergence of the truncated geometric RTF distribution, and give an explicit formula for the corresponding regularized geometric RTF distribution (the fine geometric expansion).

    This work is part of a long-term joint project with Spencer Leslie to stabilize the relative trace formula for the $\mathrm{SL}_2$-Galois period, and systematically investigate the simplest instance of so-called relative $L$-indistinguishability.

In Progress

  • “Endoscopy for the Galois Period on $\mathrm{SL}_2$: Local Results”, joint with Spencer Leslie