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.