Research Interests

PDE, Dynamical Systems, and Diffusion Propagation Theory. Key areas include:

• Propagation theory for reaction-diffusion equations;

• Monostable and bistable propagation phenomena;

• Traveling waves and spreading speeds;

• Principal eigenvalue theory;

• Nonlocal diffusion and integral operators;

• Propagation in almost periodic media;

• Free boundary problems;

• Non-classical diffusion systems;

• Connections between dynamical systems and propagation theory.

Recent work focuses on the propagation theory of diffusion systems and spectral theory of operators. Established a dynamical systems framework for monostable propagation, developed principal eigenvalue theories

for differential and integral operators, and studied anomalous propagation in complex media, revealing links

between reaction-diffusion equations, dynamical systems, ergodic theory, and spectral theory.

Selected publications appear in Comm. Pure Appl. Math., Adv. Math., J. Funct. Anal., Math. Ann., J. Math.

Pures Appl., SIAM J. Math. Anal., etc.

Current Research Focus

• Propagation in non-standard diffusion systems;

• Spectral theory of asymmetric elliptic operators on hyperbolic spaces;

• Propagation in diffusion systems generated by Lévy flights;

• Links between traveling waves and invariant foliation theory in dynamical systems