Geometric Analysis arises from the interaction of Geometry and Partial Differential Equations. Its applications cover Riemannian geometry, Topology, Complex Analysis, Physics (General Relativity) and Crystallography, among other areas. This powerful tool has been used in the resolution of deep classical problems. For instance,  Perelman has used the Ricci Flow in order to solve Poincaré's Conjecture.

In the past, this research project Geometric Analysis was supported by the Ministerio de Ciencia e Innovación (MTM2007-61775, 2007-2012) and its principal researcher was Antonio RosLater, this research project continued under the direction of Joaquín Pérez (MTM2011-22547, 2012-2014). 

Now, the research project Geometric Analysis is supported by the Ministerio de Economía y Competitividad (MTM2014-52368-P). Its principal researcher is Joaquín Pérez.