Our research focuses on the analysis of PDEs, at present particularly on the large-time behavior of parabolic and hyperbolic equations using tools from spectral theory and using entropy methods. One recent interest is on "hypocoercivity" in degenerate evolution equations. Another research direction is on the development of numerical methods for ODEs and PDEs, particularly in the context of structure-preserving schemes, efficient methods for highly-oscillatory problems, and absorbing boundary conditions. Our research is stimulated by applications in wave propagation, quantum transport (e.g. in semiconductor devices), and mechanical models.