In the extension of our research group, our goal continues to be the systematic combination of methods from analysis (e.g., variational calculus, weak convergence methods, spectral theory, and homogenisation) and probability theory (e.g., large deviations, stochastic analysis, ergodic theory, and Gibbs measures) to analyse large physical systems with complex interactions and random input. We continue to study mostly the same models as so far, such as interface models with gradient interactions, the CauchyBorn rule at positive temperatures, random media, phase boundaries with random perturbations, and interacting Brownian motions and functional integration for manybody systems. Now we will build on our achievements in the first funding period and will study deeper problems that are now within reach thanks to our recent work, like fluctuations in nonconvex perturbation of massless Hamiltonians, aging and hopping dynamics, BoseEinstein condensation, moving material singularities.
