Research Interest: I used to be a trained as a professional mathematical analyst for four years mainly concentrated on analytical properties of nonlinear partial differential equations such as wave equation with source term. Right now, I am concentrating on more applied aspect of mathematics, mainly in statistical mechanics and uncertainty quantification. Threefold problems are particularly interest me:
- Uncertainty Quantification
Determining the statistical properties of nonlinear dynamical systems is a problem of major interest in many areas of science and engineering. Even with recent theoretical and computational advancements, no broadly applicable technique has yet been developed for dealing with the challenging problems of high dimensionality, model uncertainty, lack of regularity, multi-scale features and random frequencies. My research in to systematically introduce methods in statistical mechanics, especially Mori-Zwanzig formulation, path integral method, renormalization group method to derive and simplify the exact evolution equation for probability density function of specific dynamical systems.
- Non-equilibrium statistical mechanics
Methods in uncertainty quantification I am interested in comes from the classic non-equilibrium statistical mechanics. Further detection in this field reveals deeper link between the statistical mechanics and high dimensional statistical dynamical systems which might provide us new perspectives of the classic non-equilibrium statistical mechanics. Some results might be used in detecting old, complicated problems such as the ergodicity assumption and turbulence.
- Further topics of mathematical physics
Quantum field theory and statistical field theory are particularly interesting because of their broad application and theoretical profundity. Their connection with problems of information contraction from high dimensional or infinite dimensional dynamical system is broadly noticed while limited understood. This is also a very interesting research direction I am interested to detect in the future