Professor Diogo Aguiar Gomes

IAS Fellow at Stephenson College, January – March 2025


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Diogo Aguiar Gomes, a Professor of Applied Mathematics at the King Abdullah University of Science and Technology (KAUST), is recognized for his contributions to Mean-field games and Hamilton-Jacobi equations. He has pioneered the integration of Mean Field Game theory with price models, including both theoretical aspects and numerical ones, notably through the application of Machine Learning architectures. His work in regularity theory and monotonicity methods for mean-field games, and his research on Aubry-Mather theory, especially regarding selection principles and large-time behaviour for Hamilton-Jacobi-Bellman equations, has greatly advanced the understanding of these topics. 

Professor Gomes has authored numerous influential papers. His recent publications have focused on innovative applications of Mean Field Game theory in financial mathematics, comprehensive studies of large-time profiles for Hamilton-Jacobi-Bellman equations, and investigations into the existence of solutions for stationary mean-field games through variational inequalities. These works have been featured in journals such as the SIAM Journal of Financial Mathematics, Mathematische Annalen , and the SIAM Journal on Mathematical Analysis, to name just a few. His research papers have been realized in collaboration with researchers worldwide, such as Hiroshi Mitake from the University of Tokyo, Hung Tran from the University of Wisconsin-Madison, and Filippo Cagnetti from the University of Sussex. Additionally, Professor Gomes has authored several books. These include “Regularity theory for mean-field game systems,” published by Springer in 2016, “Economic models and mean-field games theory,” and  “Viscosity solutions of Hamilton-Jacobi equations,”   published by the Instituto Nacional de Matemática Pura e Aplicada (IMPA), Rio de Janeiro in 2015 and 2009 

As an IAS Fellow, Professor Gomes will embark on a multidisciplinary project addressing income inequality and poverty using a new class of macroeconomic models based on mean-field games theory. The project aims to facilitate interdisciplinary discussions in Durham, intending to generate world-leading research and create an international research hub focused on inequality and poverty. Professor Gomes’ collaboration with Dr Alpár Meszaros and Dr Mauro Bambi will be instrumental in accomplishing these goals. 

Professor Gomes’s contributions to the field have been recognized through various awards and recognitions, including a plenary lecture at the Canadian Applied and Industrial Mathematics Society Annual Meeting and the Morrey Prize from UC Berkeley. His paper, “A Stochastic Analog of Aubry-Mather Theory,” was selected for inclusion in the IOP Select. Gomes is also an editor of various mathematical journals including SIAM J. Mathematical Analysis, Journal of Dynamics and Games, Journal of Dynamic Games, Minimax Theory and its Applications. 

Professor Gomes earned his Ph.D. in Mathematics from the University of California, Berkeley, in 2000, and his Habilitation in Mathematics from the Technical University of Lisbon in 2006. After his doctorate, he was a Postdoc at the Institute for Advanced Studies in Princeton and served as a Bing Instructor at the University of Texas at Austin. Over the years, Gomes has been invited to speak at multiple conferences, sharing his expertise in Mean-field games, reflecting his significant standing in the international mathematical community.