csrc.jpg
navigation

Research


      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


    1. Accurate and efficient computations of stochastic gene networks
    2. Emergent behaviors of stochastic gene networks
    3. Poisson representation of stochastic gene networks
    4. Parameter inference, model selection, and network inference based on single-cell data

      Mathematical theory of single-cell stochastic gene expression


    5. Discrete, continuous, and hybrid modeling of stochastic gene expression

    6. Analytical distributions of mRNA and protein fluctuations

    7. Analytical distributions of first passage times

    8. Steady-state and dynamical phase diagrams

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


    10. Frequency domain analysis of mRNA and protein fluctuations

    11. Analytical distributions of mRNA and protein fluctuations

    12. Analytical distributions of cell size

    13. Emergent concentration homeostasis

    14. Emergent cell-size homeostasis

    15. Theory of stochastic processes


    16. Multiscale model reduction

    17. Circulation theory for Markov processes

    18. Limit theorems for stochastic biochemical networks

    19. Large deviations for stochastic biochemical networks

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

    21. Nonequilibrium stochastic thermodynamics of molecular systems


    22. Fluctuation relations

    23. Fluctuation-dissipation relations

    24. Thermodynamics inference based on coarse-grained observations