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 …

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 introduce the setting of extended metric–topological measure spaces as a general
“Wiener like” framework for optimal transport problems and nonsmooth metric analysis in …

We construct a canonical differential structure on the configuration space $\Upsilon $ over a
singular base space $ X $ and with a general invariant measure $\mu $ on $\Upsilon $. We …

The notion of tamed Dirichlet space was proposed by Erbar, Rigoni, Sturm and Tamanini as
a Dirichlet space having a weak form of Bakry-\'Emery curvature lower bounds in distribution …

We develop a unifying theory for four different objects:(1) infinite systems of interacting
massive particles;(2) solutions to the Dean-Kawasaki equation with singular drift and space …

We develop a theory of optimal transport for stationary random measures with a focus on
stationary point processes and construct a family of distances on the set of stationary …

We show that a differential structure associated with the infinite particle Dyson Brownian
motion satisfies the Bakry-\'Emery nonnegative lower Ricci curvature bound $\mathsf …

The notion of tamed Dirichlet space by distributional lower Ricci curvature bounds was
proposed by Erbar, Rigoni, Sturm and Tamanini as the Dirichlet space having a weak form …

Let $\varUpsilon $ be the configuration space over a complete and separable metric base
space, endowed with the Poisson measure $\pi $. We study the geometry of $\varUpsilon …