# Curvatures of Graphs, Simplicial Complexes and Metric Spaces

Curvature is a notion originally developed in differential and Riemannian geometry. It was then discovered that curvature inequalities in Riemannian manifolds are equivalent to other geometric properties, like triangle comparison theorems, generalized Bocher inequalities, volume growth estimates, coupling of Brownian motions, or optimal transport inequalities that are meaningful on more general classes of metric spaces. Exploring this has been a major theme of mathematical research in recent years. This has provided new insight also on such classical objects as graphs and simplicial complexes, for instance by new eigenvalue estimates or Li-Yau type inequalities. In general, it has inspired the research on the geometry of metric spaces in novel ways. We want to explore this in this workshop, by bringing together experts on the different aspects of this line of research.

**Organizers**

Name | University |
---|---|

Juergen Jost | Max-Planck Institute for Mathematics in the Sciences, Germany |

BoBo Hua | Fudan University, China |