Metric measure spaces with synthetic Ricci bounds have attracted great interest in recent
years, accompanied by spectacular breakthroughs and deep new insights. In this survey, I …

We have created a functional framework for a class of non-metric gradient systems. The
state space is a space of nonnegative measures, and the class of systems includes the …

We review a class of gradient systems with dissipation potentials of hyperbolic-cosine type.
We show how such dissipation potentials emerge in large deviations of jump processes …

We formulate a class of mean field games on a finite state space with variational principles
resembling those in continuous-state mean field games. We construct a controlled continuity …

This is the first of a series of papers devoted to a thorough analysis of the class of gradient
flows in a metric space (X, d) that can be characterized by Evolution Variational Inequalities …

We study a class of nonlocal partial differential equations presenting a tensor-mobility, in
space, obtained asymptotically from nonlocal dynamics on localising infinite graphs. Our …

We consider discrete porous medium equations of the form\partial_t\rho_t=\Delta\phi
(\rho_t), where\Delta is the generator of a reversible continuous time Markov chain on a finite …

Consider the Monge-Kantorovich problem of transporting densities $\rho_0 $ to $\rho_1 $
on $\mathbb {R}^ d $ with a strictly convex cost function. A popular relaxation of the problem …

We study the nonlinear Fokker-Planck equation on graphs, which is the gradient flow in the
space of probability measures supported on the nodes with respect to the discrete …

We consider dynamics driven by interaction energies on graphs. We introduce graph
analogues of the continuum nonlocal-interaction equation and interpret them as gradient …