Research

This research area focuses on ordinary differential equations, partial differential equations, integral equations and dynamical systems. The model equations they investigate draw from robust foundations in diverse disciplines, including fluid dynamics, kinetic theory, quantum mechanics, synaptically coupled neuronal networks, and chemistry, among others. We develop and utilize various innovative ideas, methods, techniques in analysis to obtain valuable results with significant practical applications in the natural sciences and engineering.

This research area studies both algebraic combinatorics and graph theory. In graph theory, research includes sufficient conditions for Hamiltonian cycles as well as characterizations for NP hard problems when restricted to structured graph classes. In algebraic combinatorics, research includes combinatorial interpretation of integers which arise in the study of symmetric functions, quasisymmetric functions, Hecke algebras, and totally nonnegative matrices.