Research output per year
Research output per year
Personal profile
Research Overview
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.
Key Research Areas
Applied Mathematics and Computational Science
Expertise related to UN Sustainable Development Goals
In 2015, UN member states agreed to 17 global Sustainable Development Goals (SDGs) to end poverty, protect the planet and ensure prosperity for all. This person’s work contributes towards the following SDG(s):
Education
Mathematics, Habilitation, University of Lisbon
2006
Award Date: Jan 1 2006
Mathematics, Ph.D., University of California at Berkeley
2000
Award Date: Jan 1 2000
Mathematics, M.S., University of Lisbon
1996
Award Date: Jan 1 1996
Physics Engineering, B.S., University of Lisbon
1995
Award Date: Jan 1 1995
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Collaborations and top research areas from the last five years
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Algorithmic Detection of Conserved Quantities for Finite-Difference Schemes
Gomes, D. A., Krannich, F., Majrashi, B. & Ribeiro, R. D. L., Dec 2024, In: Mathematics in Computer Science. 18, 4, 21.Research output: Contribution to journal › Article › peer-review
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A mean-field game model of price formation with price-dependent agent behavior
Aljadhai, K., Almarhoumi, M., Gomes, D. & Ucer, M., 2024, (Accepted/In press) In: Sao Paulo Journal of Mathematical Sciences.Research output: Contribution to journal › Article › peer-review
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C1,α regularity for stationary mean-field games with logarithmic coupling
Bakaryan, T., Di Fazio, G. & Gomes, D. A., Sep 2024, In: Nonlinear Differential Equations and Applications. 31, 5, 90.Research output: Contribution to journal › Article › peer-review
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First-order mean-field games on networks and Wardrop equilibrium
Al Saleh, F., Bakaryan, T., Gomes, D. & de Lima Ribeiro, R., 2024, In: Portugaliae Mathematica. 81, 3-4, p. 201-246 46 p.Research output: Contribution to journal › Article › peer-review
Open Access1 Scopus citations -
VARIATIONAL APPROACH FOR PRICE FORMATION MODELS IN ONE DIMENSION
Ashrafyan, Y., Bakaryan, T., Gomes, D. & Gutierrez, J., 2024, In: COMMUNICATIONS IN MATHEMATICAL SCIENCES. 22, 1, p. 227-255 29 p.Research output: Contribution to journal › Article › peer-review
Open Access -
A Duality Approach to a Price Formation MFG Model
Ashrafyan, Y., Bakaryan, T., Gomes, D. & Gutierrez, J., 2023, In: Minimax Theory and its Applications. 8, 1, p. 1-36 36 p.Research output: Contribution to journal › Article › peer-review
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A Random-Supply Mean Field Game Price Model*
Gomes, D., Gutierrez, J. & Ribeiro, R., Feb 2023, In: SIAM Journal on Financial Mathematics. 14, 1, p. 188-222 35 p.Research output: Contribution to journal › Article › peer-review
2 Scopus citations -
Machine Learning Architectures for Price Formation Models
Gomes, D., Gutierrez, J. & Laurière, M., Aug 2023, In: Applied Mathematics and Optimization. 88, 1, 23.Research output: Contribution to journal › Article › peer-review
Open Access2 Scopus citations
Prizes
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First prize in the V, VII e VIII Portuguese Mathematical Olympiads
Gomes, D. (Recipient), 1987
Prize: Award or Honor › Early Career or Student Award
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Honorable mention in the XXX International Mathematical Olympiads - Braunschweig, Alemanha
Gomes, D. (Recipient), 1989
Prize: Award or Honor › Early Career or Student Award
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The paper "A Stochastic Analog of Aubry-Mather theory", Nonlinearity, 15 no. 3 (2002), pp. 581-603, was selected for inclusion in the IOP Select
Gomes, D. (Recipient), 2002
Prize: Award or Honor › Best Article Award
Press/Media
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New Machine Learning Study Findings Reported from King Abdullah University of Science and Technology (KAUST) (Machine Learning Architectures for Price Formation Models)
08/9/23
1 item of Media coverage
Press/Media: Press / Media