Research Interests
Research Interests
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I am a mathematician specializing in stochastic processes and their applications, especially to biology. My research interests span a broad range of topics in probability theory, including diffusion processes, branching and exchangeable particle systems, and random measure-valued processes.
Here we see a family of coalescing random walks on an ancestral graph. This is the scaling limit for the quenched limit of coalescing random walks on the pedigree generated by a diploid Moran model with selfing.
Publications and preprints
Publications and preprints
I am presently thinking about various conditional coalescent models and the (non-)robustness of their limits, especially in the context of the evolution of self-fertilization.
"Gene genealogies in a diploid Moran model with selfing conditional on its pedigree" with Wai-Tong (Louis) Fan and John Wakeley
"Quenched limit laws for the coalescent of a diploid exchangeable population model with overlapping generations" (in preparation) with Wai-Tong (Louis) Fan and John Wakeley
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 Wai-Tong (Louis) Fan
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Slides and posters
Slides and posters
Quenched limits for the coalescent of a diploid exchangeable population model with overlapping generations, Ph.D. Defense, IUB, July 2025
A modern perspective on coalescent theory and multi-locus population genetics, Population Genetics and Computational Biology Seminar, UChicago, December 2024
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