The Applied Mathematics Group in the Department of Mathematics at the University of Georgia has scientific interests in Mathematical Biology, Mathematical Ecology, Computational Mathematics, Approximation Theory, Dynamical Systems, Signal Processing, Control Theory, and Mathematical Finance. The research topics its members are currently investigating include epidemiology and systems biology of malaria, stability in population dynamics models, systems ecology, network analysis, microbial community analysis, compressive sensing, video restoration, stochastic filtering, and multivariate spline methods for applications such as numerical solutions of partial differential equations, scattered data interpolation and fitting, and image analysis.
Much of my work has been in the area of integrable Hamiltonian systems. In general I am interested in properties and applications of differential equations.
My current research interests are 1) GBC(generalized barycentric coordinates) for polygonal splines; 2) Matrix and Data Tensor Completion; 3) Numerical Solution of Helmholtz equation and Maxwell equations; 4) Graph Clustering and Semi-supervised Learning, as well as 5) Scattered Data Fitting.
Applied Mathematics, Applied Probability, Stochastic Optimal Control, Nonlinear Filtering, Mathematical Finance