2006, Habilitation in Mathematics, Universidade Tecnica de Lisboa, Portugal
2000, Ph.D. in Mathematics, University of California at Berkeley, USA1996, M.Sc. in Mathematics, Instituto Superior Tecnico, Portugal1995, B.Sc. in Physics Engineering, Instituto Superior Tecnico, Portugal
Professor Gomes’s research interests are in partial differential equations (PDE), namely on viscosity solutions of elliptic, parabolic and Hamilton-Jacobi equations as well as in related mean-field models. This area includes a large class of PDEs and examples, ranging from classical linear equations to highly nonlinear PDEs, including the Monge-Ampere equation, geometric equations for image processing, non-linear elasticity equations and the porous media equation. His research is motivated directly or indirectly by concrete applications. These include population and crowd modeling, price formation and extended mean-field models, numerical analysis of infinite dimensional PDEs and computer vision.
Before joining KAUST, Professor Gomes has been a Professor in the Mathematics Department at the Instituto Superior Tecnico since 2001. He did his Post-Doc at the Institute for Advanced Study in Princeton in 2000 and at the University of Texas at Austin in 2001.