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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
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
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
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
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
Fluctuation relations
Fluctuation-dissipation relations
Thermodynamics inference based on coarse-grained observations
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