A discrete surface is a simplicial complex which is locally isometric to $R^2$ or upper half plane, and we can define Gaussian curvature and circle packing metric on it, then we’ll explain the discrete Gauss-Bonnet theorem. Also, we can compute the relation between length of simplices and the metric and define Ricci flow, then I’ll prove the convergence of the discrete Ricci flow.

Professor Maria J. Esteban is a Basque-French mathematician. In her research, she studies nonlinear partial differential equations, mainly by the use of variational methods, with applications to physics and quantum chemistry. She has also worked on fluid-structure interaction. She did her PhD thesis at the Pierre and Marie Curie University (Paris), under the direction of Pierre-Louis Lions. After graduation, she became full-time researcher at CNRS, where she holds now a position of director of research. From 2015 to 2019, she is president of International Council for Industrial and Applied Mathematics (ICIAM). She was president of the Société de Mathématiques Appliquées et Industrielles from 2009 to 2012 and chair of the Applied Mathematics Committee of the European Mathematical Society in 2012 and 2013. She participated in the Forward Look on "Mathematics and Industry" funded by the European Science Foundation and is one of the launchers of the EU-MATHS-IN European network for industrial mathematics.