Research

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My research is centered on applied mathematics, biomathematics, stochastic processes, and stochastic thermodynamics. I apply modern mathematical frameworks --- including probability theory, stochastic processes, differential equations, dynamical systems, mathematical statistics, functional analysis, and graph theory --- to develop rigorous analytical theories, novel statistical inference methods, and efficient computational techniques for stochastic gene regulatory networks and biochemical reaction networks. My ultimate goal is to understand the stochastic dynamics and thermodynamics of complex cellular and subcellular processes that operate far from equilibrium and across multiple timescales. This is a highly interdisciplinary field at the forefront of contemporary scientific research.

In addition to my interdisciplinary efforts, I am also focused on developing new and abstract mathematical theories with applications to the natural sciences. Key areas of interest include Markov processes, semi-Markov processes, non-Markov processes, large deviation theory, stochastic analysis, and queueing theory.

Stochastic dynamics of complex gene regulatory networks

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1. Accurate and efficient computations of stochastic gene networks

   Emergent behaviors of stochastic gene networks

   Poisson representation of stochastic gene networks

   Parameter inference, model selection, and network inference based on single-cell data

   Mathematical theory of single-cell stochastic gene expression

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   Discrete, continuous, and hybrid modeling of stochastic gene expression

   Analytical distributions of mRNA and protein fluctuations

   Analytical distributions of first passage times

   Steady-state and dynamical phase diagrams

   Coupled stochastic dynamics of gene expression, cell size, and cell cycle

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   Frequency domain analysis of mRNA and protein fluctuations

   Analytical distributions of mRNA and protein fluctuations

   Analytical distributions of cell size

   Emergent concentration homeostasis

   Emergent cell-size homeostasis

   Theory of stochastic processes

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   Multiscale model reduction

   Circulation theory for Markov processes

   Limit theorems for stochastic biochemical networks

   Large deviations for stochastic biochemical networks

   Semi-Markov processes, non-Markov processes, and queueing theory

   Nonequilibrium stochastic thermodynamics of molecular systems

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2. Fluctuation relations

3. Fluctuation-dissipation relations

4. Thermodynamics inference based on coarse-grained observations