I am presently thinking about various families of random walks in random environments that arise in the study of population genetics. In particular, I wish to understand how genetic variation across the genome is limited by the existence of the organismal pedigree as a latent variable constricting the evolution of gene genealogies. This includes ongoing work on quenched ARGs, large sample limits for quenched coalescents, and understanding how pedigrees affect biobank scale datasets with various collaborators. The following are available preprints:

"The quenched structured coalescent for diploid populations on finite graphs with large migrations and uneven offspring distributions."

"Quenched coalescent for diploid population models with selfing and overlapping generations" with Louis Wai-Tong Fan and John Wakeley.

"Gene genealogies in a diploid Moran model with selfing conditional on its pedigree" with Wai-Tong (Louis) Fan and John Wakeley. Theoretical Population Biology. Volume 165, October 2025, Pages 29-44.

I have also been independently investigating geometric rigidity results arising from exchangeability of random variables:

"Rigidity of infinite exchangeable sequences of Gaussian random variables" (in preparation.)

I am also interested in various aspects of understanding the fitness landscape for biological populations. In the simplest sense, this landscape is modeled by solutions to the Fisher-Kolmogorov-Petrovsky-Piskuonov (FKPP) equation. I have been working on extending classical results on equations of KPP type to other geometric domains:

"Traveling wave profiles and asymptotics for equations of KPP type in warped product spaces'" (in preparation) with Louis Wai-Tong Fan.