Research

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My research focuses on applied mathematics, mathematical life sciences, and stochastic processes. I am using modern mathematical theory (probability theory, stochastic processes, differential equations, dynamical systems, spectral theory, graph theory, and statistics) to develop novel analytical theory and efficient computational methods of stochastic gene regulation networks and biochemical reaction networks, with the aim of understanding the stochastic dynamics and thermodynamics of complex cellular and subcellular processes far from equilibrium and with multiple time scales. This is a hotspot research field with highly interdisciplinary features.

I am not only carrying out interdisciplinary research, but also actively engaged in high-level mathematical research with the aim of developing new mathematical theories related to natural sciences with full rigor and a high degree of abstraction. Some of the mathematical topics include Markov and semi-Markov processes, large deviation theory, stochastic analysis, and queuing theory.

Stochastic dynamics of complex gene regulatory networks

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1. Accurate and efficient computations of stochastic gene networks

   Emergent properties of stochastic gene networks

   Poisson representation of gene networks

   Parameter inference and model selection 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 numbers

   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 for lineage measurements

   Analytical distributions of mRNA and protein numbers/concentrations

   Analytical distributions of cell size

   Emergent concentration homeostasis

   Emergent cell-size homeostasis

   Theory of stochastic processes

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   Multiscale model reduction

   Loop-erased circulation theory for Markov processes

   Limit theorems of stochastic chemical reaction networks

   Freidlin-Wentzell-type large deviations

   Donsker-Varadhan-type large deviations

   Maximal inequalities for Markov processes

   Nonequilibrium stochastic thermodynamics of molecular systems

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2. Cycle currents of molecular systems

3. Entropy production of molecular systems

4. Fluctuation relations

5. Fluctuation-dissipation relations