Metastability, relaxation, and coarsening
On the shape of complex energy landscapes
We are interested in describing and quantifying the shape of complex energy landscapes, in particular as it relates to the qualitative and quantitative behavior of the corresponding gradient flows, with and without the presence of a random perturbation. To this end we use tools coming from the fields of analysis, partial differential equations, and probability theory.
Work related to the shape and dynamics of PDE energy landscapes includes the study of optimal relaxation rates for gradient flows with respect to a nonconvex energy, properties of the Cahn-Hilliard energy landscape for large systems and mean value close to -1, and dynamic metastability of gradient flows.
The interplay between small noise and large system size is an additional area of interest.