Seminario de geometría, álgebra y topología (GATO)

Christian Ketterer, U. de Freiburg, Alemania.

Modalidad: Presencial.

Resumen: Motivated by Gromov's precompactness theorem, Lott-Villani and Sturm introduced around 15 years ago the idea of synthetic lower Ricci curvature bounds. Via this approach one can give a meaning to lower Ricci curvature bounds for metric measure spaces, completely independent of an underlying smooth structure. This theory is based on optimal transport and the properties of entropy functionals on the space of probability measures, and it has been further refined in the last years by numerous authors.

In this talk I will give a brief introduction to the main concepts of this theory and will present some of its consequences, focusing on geometric results with applications to smooth Riemannian manifolds.