I am interested in following research projects which are significant for leading to Ph.D. dissertations in mathematical biology.

(1) Energy-Balanced Biochemical Systems. Lambda Phage, Cell Cycle, and Phototransduction.

(2) Mathematical Theory of Nonlinear DNA Elasticity. Both deterministic and stochastic approaches will be employed.

(3) Mathematical Theory of Ionic Distribution around Cylindrical Molecules and Its Applications to DNA. ODE and its asymptotic analysis, numerical investigation, and Painleve equation.

(4) Mathematical Foundation of Fluorescence Correlation Spectroscopy and Its Related Methods. Including high-order time correlation function and generalization of Green-Kubo formulae.

(5) Protein Folding and Its Related Mathematical Problems. Kinetics in energy landscape, dimension reduction and simplex search, and relation to mutual information.

(6) Fluctuating Nonlinear Biochemical Reactions and Stochastic Resonance. Birth-death processes and Brownian motion, nonlinear oscillation, and phase space analysis: developing a stochastic version of the Wymann-DiCera kinetic network (hypercycle) and show its nonlinear stochastic behavior as well as SR.

(7) Stochastic Macromolecular Mechanics, Nonequilibrium Thermodynamics, and Their Applications. Brownian motion, large deviation theory, and nonlinear diffusion equation.

(8) An Algebreic-Topological Approach to Irreversible Markov Processes. Graph and network theory, asymmetric linear operator and its eigenvalues, non-normal matrix, and Markov processes.