My research is in probability and analysis, with a focus on Schramm-Loewner Evolution (SLE). I particularly like problems with links to statistical physics, including those involving Dyson Brownian motion, random matrix theory, and superprocesses. I’ve also worked on some collaborations in stochastic arithmetic dynamics.
Papers in Loewner Evolution/SLE:
- Large deviations of Dyson Brownian motion on the circle and multiradial SLE0+ (with Osama Abuzaid and Eveliina Peltola). Preprint. [arxiv]
- Scaling limits of branching Loewner evolutions and the Dyson superprocess (with Govind Menon). Pacific Journal of Math, to appear. [arxiv]
- N-Sided radial Schramm-Loewner evolution (with Gregory F. Lawler). Probab. Theory Relat. Fields 181, pages 451–488 (2021). [arxiv]
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., 176.1 (2024): 95-122. [arxiv]
- Stochastic canonical heights (with Wade Hindes). J. Number Theory, 201 (2019): 228-256. [arxiv]