Overview
My research is in the area of probability and partial differential equations, which have been used to model many phenomena in the natural sciences and engineering. Asymptotic analysis has been a common theme in much of my research. Current research interests include: stochastic dynamics, interacting particle systems, reaction-diffusion equations, applications to biological models.
Current Appointments & Affiliations
Professor of Mathematics
·
2021 - Present
Mathematics,
Trinity College of Arts & Sciences
Recent Publications
Local collective memory from ratiometric signaling outperforms cellular gradient sensing limits
Preprint · April 24, 2025 Featured Publication Full text CiteUSING BERNOULLI MAPS TO ACCELERATE MIXING OF A RANDOM WALK ON THE TORUS
Journal Article Quarterly of Applied Mathematics · January 1, 2024 Featured Publication We study the mixing time of a random walk on the torus, alternated with a Lebesgue measure preserving Bernoulli map. Without the Bernoulli map, the mixing time of the random walk alone is O(1/ε2), where ε is the step size. Our main results show that for a ... Full text CiteThe Fleming-Viot Process with McKean-Vlasov Dynamics
Journal Article Electronic Journal of Probability · August 3, 2022 Featured Publication The Fleming-Viot particle system consists of N identical particles diffusing in a domain U⊂Rd. Whenever a particle hits the boundary ∂U, that particle jumps onto another particle in the interior. It is known that this system provides a particle representat ... Full text Link to item CiteRecent Grants
RTG: Training Tomorrow's Workforce in Analysis and Applications
Inst. Training Prgm or CMECo-Principal Investigator · Awarded by National Science Foundation · 2021 - 2026Support for Southeastern Probability Conference
ConferenceCo Investigator · Awarded by National Science Foundation · 2020 - 2024CAREER: Research and training in stochastic dynamics
ResearchPrincipal Investigator · Awarded by National Science Foundation · 2014 - 2020View All Grants
Education, Training & Certifications
University of Texas, Austin ·
2006
Ph.D.
Davidson College ·
2000
B.S.