1) Phase transition and metastability\n* Criteria for metastability (potential theory, capacities)\n* convergence rate analysis of sampling algorithms\n* classification and bifurcation analysis of phase transitions in models of interacting particles/ agents (consensus finding)\n*André Schlichting, Christian Seis. Analysis of the implicit upwind finite volume scheme with rough coefficients. Numer. Math., 2017. nucleation, condensation, coarsening and oscillation phenomena in growth processes\n\n2) Gradient flows on general state spaces\n* Variational formulation of discrete and nonlocal evolution equations (continuum limits)\n* mountain-pass theorems in metric spaces (space of probability measures)\n* applications to data science\n\n3) Variational analysis in stochastic and numerical analysis\n* convergence rates of finite volume schemes\n* coarse-graining (dimension reduction) of molecular dynamics\n* heat kernel bounds via theory of large deviations and optimal transport