Bio
- Since 2015, I have held the position of full Professor at the Complutense University of Madrid in the Department of Theoretical Physics. From 2019 to 2023, I was a faculty member of the Instituto de Ciencias Matemáticas (ICMAT). From 2020 to 2022, I served as a member of the Government Board of the Royal Spanish Mathematical Society (RSME).
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My fields of research are mathematical physics and applied mathematics. In particular, I have been actively involved in the theory of integrable systems, the field of othogonal polynomials, and special functions theory. Recently, we have provided a complete representation of the classical multiple orthogonal polynomials and their corresponding recursion coefficients in terms of hypergeometric series and the Mellin transform, thereby closing a long-standing open problem in the field. Almost simultaneously, we have established a spectral theorem in the spirit of Favard for bounded banded operators, extending the well-known spectral Favard theorem for Jacobi matrices.
I have also conducted investigations on random walks and Markov chains beyond birth and death. Other research interests include the application of the Riemann—Hilbert problem in characterizing non-Abelian Painlevé discrete equations and the use of the Gauss—Borel factorization of semi-infinite Gram matrices to discover Christoffel and Geronimus formulas in various extended orthogonalities. I have studied orthogonalities in the following forms: discrete, matrix, multivariate, mixed multiple, and Sobolev. The relationship between new integrable systems or families of solutions and these orthogonal systems has also been a significant focus of my studies.
- I have coauthored 139 scientific publications, out of which 108 are published in JCR journals, with 65 of them in first quartil. Presently, I am leading a Spanish National Plan project, and in the past, I have led two additional Spanish National Plan projects, all within the field of Mathematics. Furthermore, I have been a member of six international research projects and ten national research projects. I have supervised three PhD theses and I am currently supervising two more. Additionally, I have organized R&D&I activities, including international scientific conferences.
- Together with Luis Martínez-Alonso, I recently completed a comprehensive book titled Boundary Value Problems for Linear Partial Differential Equations, published by CRC Press, a renowned and respected publisher in the academic community. The book, available at DOI:10.1201/9781032664514 aims to provide a valuable resource for students, researchers, and practitioners interested in exploring the fascinating realm of linear partial differential equations and their boundary value problems. We hope this work will contribute to the advancement of knowledge in this field and serve as a helpful reference for those seeking a deeper understanding of these complex mathematical concepts.
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I have supervised 8 Master's Theses, 11 Bachelor's Theses, and 2 academically directed projects. Additionally, I have been responsible for 40 teaching groups, all within the field of Mathematical Physics and Mathematics. My teaching focuses on courses related to partial differential equations in Mathematical Physics, including boundary value problems, as well as the fundamentals of complex analysis in one variable and its applications. I have also taught postgraduate courses covering topics such as group theory, Kac-Moody algebras, functional analysis, integrable systems, and orthogonal polynomials.
Furthermore, I am the author of two teaching manuals on Differential Equations and another one on Complex Analysis. I have actively participated in 5 teaching innovation projects, and for four years, I served as an evaluator of educational innovation projects at the Autonomous University of Madrid. Additionally, I have contributed to pre-university orientation activities and collaborated in university entrance exams. Specifically, I have served as a member twice, deputy secretary three times, and vice president eight times at various venues.
- I have organized 6 meetings on the European Higher Education Area, published 2 works on European convergence, and delivered 9 presentations on university teaching. I actively participated, representing the area of Theoretical Physics, in the work group responsible for developing the current study plan for the Physics degree at the UCM. Lastly, I have served on the executive committee of MiriadaX, a MOOC platform promoted by Universia.
- In terms of administration, I have held various positions, including Vice Dean, advisor to the Vice Chancellor for the Direction of the European Convergence Office, Director of the Department of Theoretical Physics II, Deputy Vice Chancellor of Innovation, and Coordinator of the Doctoral Program in Physics. I am an active member of the Faculty Board, the University Senate, and the Statutes Commission of the University Senate.