Probability Theory and Applied Stochastic Processes

Remarkable progress in advanced microscopy has yielded unprecedented access to a path-wise observation of fundamental stochastic processes such as the motion of invasive particulates in viscoelastic fluids; the kinetics of strands of DNA and semi-flexible polymers; and the mechanics of intracellular transport. In each case, stochasticity is unmistakeable and essential. Most important, because we are looking at data from a relatively new field, when one extracts tractable but qualitatively authentic models, the analysis inevitably calls for new mathematics. In my own work, I have dealt with systems involving complex self-interactions, long-term memory effects and non-equilibrium dynamics.

Generally speaking, I am interested in analyzing qualitative properties of stochastic differential equations and stochastic partial differential equations that model biological phenomena. Specifically I have studied sub-diffusive behavior in diffusing particles that are subjected to viscoelastic response from their environment; ergodicity of passive interacting particles that are being advected by a stochastic Stokes fluid; and small-scale and large-scale transport properties of processive molecular motors.

Key Links

--  I organize the Biomath Seminar. We meet weekly on Tuesdays at 12:50.

--  I am currently teach Probability and Potential Theory.

Recent News

--  My joint work with Andrew Hein on animal search has now appeared in the journal, PNAS.  The work was featured by the UF Research News blog, “University of Florida researchers improve on an old model for studying predator search patterns.”

    For background discussion and context, please visit this entry on my general interest blog.

-- This summer I was invited to give two lectures at the Joint MBI-NIMBioS-CAMBAM Workshop on Stochastics Applied to Biological Systems.

    Lecture 1:  ”Diffusion in Biological Media.”

    Lecture 2: “The Mathematics of Intracellular Transport.”

    For the abstract and further information, please visit here.