Summary
Broadly speaking, my current research focuses on stochastic and non-equilibrium processes, with particular applications to molecular and cell biology. My work draws upon a wide range of analytical tools and mathematical methods, including probability theory and stochastic processes, non-equilibrium statistical physics, partial differential equations, dynamical systems theory, and nonlinear patterns and waves.
Current research topics include the following: mean field theory and interacting particle systems, stochastic processes with resetting, stochastic calculus in bounded domains (partially absorbing targets, semi-permeable membranes, sticky boundaries), stochastic thermodynamics, active particles, cellular diffusion in singularly perturbed domains, cytoneme-based morphogenesis and viral spread, applications of queueing theory to intracellular transport processes, stochastically switching (hybrid) systems, active phase separation, and protein aggregation. I also have a long-standing interest in neural field theory and models of visual cortex.
In 2014 I published the first graduate textbook on "Stochastic Processes in Cell Biology" (Springer 2014). A two-volume 2nd edition appeared in 2021.
Paul C. Bressloff Volume I: Molecular Processes Interdisciplinary Applied Mathematics 41 (Springer) (2021)
Paul C. Bressloff Volume II: Cellular Processes Interdisciplinary Applied Mathematics 41 (Springer) (2021)
From 2001-2023 I was a senior faculty member of the graduate program in mathematical biology at the University of Utah. This program was one of the first of its kind in the US, and many of its graduate alumni are now mathematical biology faculty.
Recent Papers
P. C. Bressloff. Random search with stochastic resetting: when finding the target is not enough. Submitted (2025)
P. C. Bressloff. Diffusion-mediated adsorption versus absorption at partially reactive targets: a renewal approach. Submitted (2025)
P. C. Bressloff. Encounter-based model of a run-and-tumble particle with stochastic resetting. Submitted (2025)
P. C. Bressloff. Slow-fast systems with stochastic resetting. Submitted (2025)
P. C. Bressloff. Stochastic calculus of run-and-tumble motion: an applied perspective. Submitted (2025)
P. C. Bressloff. Kuramoto model with stochastic resetting and coupling through an external medium. Chaos 35 023162 (2025)
P. C. Bressloff. Cellular diffusion processes in singularly perturbed domains. Special issue: Problems, progress and perspectives in mathematical and computational biology. J. Math. Biol. 89 58 (52 pages) (2024)
P. C. Bressloff. Generalized Ito's lemma and the stochastic thermodynamics of diffusion with resetting. J. Phys. A 57 445003 (2024)
P. C. Bressloff. Asymptotic analysis of particle cluster formation in the presence of anchoring sites. Eur. Phys. J. E 47 30 (2024)
P. C. Bressloff. Entropy production for diffusion processes across a semi-permeable interface. Phys. Rev. Res. 6 023283 (2024)
P. C. Bressloff. A generalized Dean-Kawasaki equation for an interacting Brownian gas in a partially absorbing medium. Proc. Roy. Soc. A 480 20230915 (2024)
P. C. Bressloff. Semi-permeable interfaces and the target problem. In. Target Search Problems. Eds. D. Grebenkov, R. Metzler and G. Oshanin Springer (2024)
P.C. Bressloff. Asymptotic analysis of particle cluster formation in the presence of anchoring sites. Eur. J. Phys. E 47 30 (2024)
P. C. Bressloff. Global density equations for interacting particle systems with stochastic resetting: From overdamped Brownian motion to phase synchronization. Chaos 34 043101 (2024)
P. C. Bressloff. Global density equations for a population of actively switching particles. J. Phys. A 57 085001 (2024)
P. C. Bressloff. Asymptotic analysis of conversion-limited phase separation. Proc. Roy. Soc. A 480 2023.0725 (2024)
P. C. Bressloff. Transition path theory for diffusive search with stochastic resetting. J. Phys. A 57 145001 (2024)
P. C. Bressloff. Truncated stochastically switching processes. Phys. Rev. E 109 024103 (2024)