Speaker: Kazuhiro Kuwae

Title: Hess-Schrader-Uhlenbrock inequality for the heat semigroup on differential forms over Dirichlet spaces tamed by distributional curvature lower bounds

Abstract: The notion of tamed Dirichlet space was proposed by Erbar, Rigoni, Sturm and Tamanini ('22) as a Dirichlet space having a weak form of Bakry-\'Emery curvature lower bounds in distribution sense. After their work, Braun (‘22+) developed a vector calculus for it, which was studied by Gigli ('18)  for ${\sf RCD}$-spaces. In this framework, I will talk about the Hess-Schrader-Uhlenbrock inequality for $1$-forms as an element of $L^2$-cotangent module  (an $L^2$-normed $L^{\infty}$-module), which  extends the Hess-Schrader-Uhlenbrock inequality by Braun ('22+) under an additional condition.