Profiles

Professor Miguel Urbano, who joined KAUST in 2022, received his Ph.D. in Mathematical Analysis in 1999 from the University of Lisbon, Portugal. Following a postdoctoral position at Northwestern University in the United States, he became an assistant professor at the University of Coimbra (UC), Portugal. He was promoted to associate professor with tenure at UC in 2004 and awarded a habilitation in mathematics in 2005, before becoming a full professor in 2009.

Professor Urbano is the author of The Method of Intrinsic Scaling, published in the Lecture Notes in Mathematics series, and over 70 scientific papers on nonlinear partial differential equations (PDEs). He has served on panels evaluating grants and research projects for the European Union, the European Research Council, the Academy of Finland, the Latvian Council of Science, the Serrapilheira Institute of Brazil, and the Portuguese Science Foundation.

Urbano served on Portugal's National Council for Science and Technology from 2012 to 2015, won the José Anastácio da Cunha Prize from the Portuguese Mathematical Society in 2002, and was an associate editor for Nonlinear Analysis from 2013 to 2021. He is a corresponding academician of the Lisbon Academy of Sciences (elected in January 2021), co-editor-in-chief of Portugaliae Mathematica (since January 2022), and a member of the editorial board of Communications in Partial Differential Equations (since February 2026).

Professor Miguel Urbano is an expert on free boundary problems and regularity theory for nonlinear PDEs, particularly on the method of intrinsic scaling for singular or degenerate-type equations.

He has made several contributions leading to a better understanding of the local behaviour of weak solutions, e.g., the derivation of a quantitative modulus of continuity for weak solutions of the two-phase Stefan problem, which models a phase transition at a constant temperature or the proof of a long-standing conjecture on the optimal regularity for solutions of the p-Poisson equation in the plane.

Rafayel Teymurazyan obtained his PhD in Mathematics from the University of Lisbon (Portugal) in 2013. After postdoc and research positions at the Federal University of Ceará (Brazil), the University of Texas at Austin (USA) and the University of Coimbra (Portugal), he joined KAUST in May of 2023. He works on regularity theory for nonlinear PDEs and the mathematical analysis of free boundary problems.

Rafayel Teymurazyan works on nonlinear  partial differential equations (PDEs) and free boundary problems. The term free boundary problem (FBP) refers to a PDE to be solved both for an unknown function and for an unknown domain. FBPs arise in range of mathematical models that are used to describe a physical or biological phenomenon (for example, ice melting into water, population dynamics), or an economical or financial occurrence (American options, stock markets).

Aelson Sobral is a postdoctoral researcher in the Free Boundary and Interface Problems group, led by Prof. Miguel Urbano at KAUST. He earned his PhD in Mathematics from the Federal University of Paraíba (UFPB), Brazil, before joining KAUST in September 2024. His research explores geometric frameworks to advance the regularity theory of fully nonlinear PDEs and Free Boundary Problems that are often born in phenomenon related to superconductivity and congested traffic dynamics.

Aelson Sobral's research centers on developing geometric tools to analyze Free Boundary Problems, focusing on regularity theory for degenerate and singular partial differential equations (PDEs) and free boundary regularity. These problems are intrinsically linked to flame propagation and congested traffic dynamics.

Nuno J. Alves is a postdoctoral researcher in the Free Boundary and Interface Problems group, led by Prof. José Miguel Urbano. He earned his PhD in Applied Mathematics and Computational Science from KAUST in 2023, under the supervision of Prof. Athanasios E. Tzavaras. Before returning to KAUST in March 2026, he was a postdoctoral researcher at the University of Vienna, working with Prof. Peter Markowich. His research lies broadly in mathematical analysis, with particular emphasis on functional analysis, harmonic analysis, the calculus of variations, and the analysis of partial differential equations.

Nuno Alves’ research focuses on mathematical analysis and its applications to nonlinear partial differential equations. His interests include functional and harmonic analysis, compactness and convergence in function spaces, fractional integral operators, asymptotic problems for PDEs, and Gamma-convergence methods in the calculus of variations. His work also involves fluid and kinetic models, including Euler-type, BGK-type, and Vlasov-type equations, with an emphasis on stability, singular limits, weak-strong uniqueness, and relative entropy methods.

Ahmed Abdali graduated from the University of Bahrain with a BSc in Mathematics in 2022.

Nonlinear PDEs and applications.

Hanan Albarqi obtained a master’s degree in Pure Mathematics from the University of Illinois at Urbana–Champaign in 2022 and a bachelor’s degree in Mathematics from King Khalid University in 2017.

Analysis and applied PDEs.

Hikmatullo Ismatov earned a Bachelor's degree in Applied Mathematics and Computer Science from Lomonosov Moscow State University (2017-2021). He joined KAUST as an MS/PhD student in 2023. Before starting his graduate studies, Hikmatullo completed an internship at KAUST in the same year.

Hikmatullo Ismatov's research centers on nonlinear PDEs, particularly the Infinity-Laplace equation. This class of equations has significant applications in understanding various optimization problems and phenomena, such as tug-of-war games and image processing. His work aims to contribute to the theory and applications of nonlinear PDEs, particularly through rigorous mathematical analysis and computational approaches.

Zahrah Alnasser obtained her bachelor's degree from Dammam College for Women and her master's degree in pure mathematics from the University of Illinois - Urbana-Champaign.

Real analysis and applied PDEs.