My research is in analysis and probability, with a focus on Schramm-Loewner Evolution (SLE) and the deterministic Loewner equation. I particularly like problems with links to statistical physics, including those involving random maps, random matrix theory, and superprocesses.
Papers in Loewner Evolution/SLE:
Large deviations of Dyson Brownian motion on the circle and multi-radial SLE0+ (with Osama Abuzaid and Eveliina Peltola). In preparation. Preprint available by request.
Scaling Limits of Branching Loewner Evolutions and the Dyson Superprocess (with Govind Menon). Preprint: arXiv:2310.02858.
N-Sided Radial Schramm-Loewner Evolution (with Gregory F. Lawler). Probab. Theory Relat. Fields 181, pages 451–488 (2021). https://doi.org/10.1007/s00440-021-01033-9
Papers in Stochastic Arithmetic Dynamics:
Galois groups and prime divisors in random quadratic sequences (with John Doyle, Wade Hindes, and Rafe Jones). Math. Proc. Cambridge Philos. Soc., 1-28, (2023). doi:10.1017/S0305004123000439
Stochastic Canonical Heights (with Wade Hindes). J. Number Theory, 201 (2019):228-256.