Curriculum Vitae - Extended Academic and Research Profile (2026)
Current affiliation: Professor of Applied Mathematics
Centro de Estudios Matemáticos
Facultad de Empresa y Tecnología
Universidad a Distancia de Madrid (UDIMA), Spain
ORCID: 0000-0001-6802-3303
Academic email: edmundojose.huertas@udima.es
I am currently Professor of Applied Mathematics at Universidad a Distancia de Madrid (UDIMA), Spain, where I joined the Centre for Mathematical Studies, Faculty of Business and Technology, on 1 October 2026.
I also hold a permanent civil-service appointment as Associate Professor (Profesor Titular de Universidad) in Applied Mathematics at the University of Alcalá (UAH), a position I held in active service from September 2020 to September 2026. I am currently on authorized temporary leave of absence from UAH under Article 17.4 of Spanish Law 14/2011 on Science, Technology and Innovation, which provides for the reservation of my permanent university position and the continued right to research assessment during the period of leave.
My academic career combines mathematical research, international scientific collaboration, competitive research funding, university teaching, doctoral supervision, and academic leadership, with a particular emphasis on connecting rigorous mathematical theory with emerging computational and technological applications.
My principal research interests lie in Mathematical Analysis, Functional Analysis, Approximation Theory, Spectral Theory, Orthogonal Polynomials, and Special Functions. In recent years, I have progressively expanded my research towards Statistical Learning Theory, Kernel Methods, Support Vector Machines (SVMs), Data Analysis, and Quantum Machine Learning (QML).
This interdisciplinary orientation is supported by my academic background in Mathematics, Physics, and Computer Science, together with research experience in both theoretical and applied problems.
My scientific work focuses primarily on the theory of orthogonal polynomials and their applications, particularly the analytical, algebraic, asymptotic, and spectral properties of classical and nonclassical families.
My contributions include the study of Krall-type and Sobolev-type orthogonal polynomials, canonical perturbations of orthogonality measures, Christoffel, Geronimus, and Uvarov transformations of measures, zero distributions, electrostatic models for zeros of orthogonal polynomials, strong and relative asymptotics, differential and q-difference equations, higher-order recurrence relations, and associated matrix factorizations.
I have also worked on multiple and mixed-type orthogonal polynomials, matrix orthogonality, and orthogonal Laurent polynomials, including their connections with CMV-type matrix representations and orthogonality on the unit circle.
My broader research collaborations encompass spectral and analytical approaches involving Riemann–Hilbert problems, bispectral structures, matrix-valued orthogonality, and transformations of structured polynomial systems. These mathematical tools provide a framework for studying problems in spectral analysis, approximation, integrable systems, and mathematical physics.
The applied dimension of my research includes digital image processing and watermarking through orthogonal moments, statistical modelling of excess mortality, and computational techniques for scientific data analysis. My participation in collaborative research projects also extends to spectral models of quasi-birth-and-death (QBD) processes, birth–death chains, random matrices, quantum computing.
A particularly important direction of my current research is the construction and mathematical analysis of structured positive-definite kernels derived from orthogonal polynomials, especially those associated with Christoffel–Darboux kernels and reproducing-kernel structures.
My objective is to connect the analytical and spectral properties of orthogonal-polynomial systems with supervised learning, classification, regression, regularization, kernel design, and Support Vector Machines, investigating their potential extensions to quantum kernels and Quantum Support Vector Machines (QSVMs).
This research programme seeks to bring mathematical structure, analytical interpretability, and computational efficiency to modern machine-learning methodologies.
To date I am the author or coauthor of 33 scientific publications, including 22 articles in journals indexed in Journal Citation Reports (JCR), of which 12 appeared in first-quartile (Q1) journals, together with five Scopus-indexed book chapters or scientific contributions.
My research has appeared in international journals including Journal of Computational and Applied Mathematics, Numerical Algorithms, Complex Variables and Elliptic Equations, Mathematics, Symmetry, Electronics, and PLOS ONE, among others.
According to Scopus data recorded in October 2026, my scientific production has an h-index of 8 and 141 citations.
I have been awarded three positively evaluated six-year research periods (sexenios de investigación) by the Spanish National Commission for the Evaluation of Research Activity (CNEAI/ANECA), corresponding to:
2008–2013
2014–2019
2020–2025
These three consecutive research assessments recognize sustained scientific activity over eighteen years.
In addition to my research publications, I have contributed extensively to the international scientific community through editorial work and peer review. I have completed 39 verified manuscript reviews recorded in Web of Science, alongside further scientific assessment and mathematical reviewing activities.
I was scientific co-editor, together with Professor Francisco Marcellán, of the Springer research volume Orthogonal Polynomials: Current Trends and Applications (SEMA SIMAI Springer Series, Volume 22, 2021). I have also served as Guest Editor of a special issue of the international journal Mathematics.
In 2013, I received the Excellence Award of Universidad Carlos III de Madrid, granted by its Social Council following an evaluation involving national and international experts.
I have participated in competitively funded research projects at national, regional, and international levels, including two projects as Principal Investigator (PI).
Among my principal achievements in competitive research funding are:
CM/JIN/2021-014 — Orthogonality and Functional Equations: Theory and Applications (2022–2023). I served as Principal Investigator of this research project funded by the Community of Madrid and the University of Alcalá, coordinating a research team focused on analytical and structural problems in orthogonality theory and functional equations.
PEJ-2023-AI/COM-28493 — New Kernel Functions from Orthogonal Polynomials in Quantum Machine Learning (2024–2026). As Principal Investigator, I led this competitively funded research initiative supported by the Community of Madrid. The project financed the recruitment of a research assistant for two years and contributed to the development of a research direction connecting orthogonal polynomials, structured kernels, classical machine learning, and quantum computational models.
I am also a member of the research team of the national project PID2024-155133NB-I00 — Orthogonality, Approximation and Integrability: Applications in Classical and Quantum Stochastic Processes (2025–2028), funded by the Spanish Ministry of Science, Innovation and Universities.
My additional research participation includes projects involving quantum stochastic processes, spectral analysis, quantum support vector machines, post-quantum cryptography, artificial intelligence, and mathematical modelling in engineering applications.
These activities reflect my commitment to combining fundamental mathematical research, competitive funding, interdisciplinary collaboration, and the development of new applications of mathematical methods.
International collaboration has been a central component of my academic career.
From 25 January 2023 to 24 January 2024, I was a full-time Visiting Researcher at the Institute of Mathematical Sciences (ICMAT-CSIC), Madrid, under the Spanish University System Recualificación Programme, funded through NextGenerationEU.
This research stay strengthened my collaborations in orthogonal-polynomial theory, multiple orthogonality, and spectral methods, while supporting the development of new mathematical approaches to kernel construction and machine learning.
Previously, I held a two-year postdoctoral research fellowship (2013–2015) at the University of Coimbra, Portugal, awarded competitively by the Fundação para a Ciência e a Tecnologia (FCT). During this period, I conducted research at the Department of Mathematics in collaboration with Professor Amílcar Branquinho and other researchers in approximation theory and orthogonal polynomials.
My international research training also includes two predoctoral stays at leading mathematical research institutions:
Georgia Institute of Technology (Georgia Tech), Atlanta, USA (2010), School of Mathematics.
KU Leuven, Belgium (2011), Department of Mathematics.
I have additionally undertaken shorter research visits and collaborations at institutions in Mexico, Poland, Portugal, and Spain.
I am co-coordinator of the research group Functional Analysis: Asymptotic Theory and Orthogonality (AnFAO) at the University of Alcalá.
I was also co-founder and co-coordinator (2021–2026) of the Ibero-American Research Network on Orthogonal Polynomials, Functional Equations and Applications (RIPOEFA), supported by the Asociación Universitaria Iberoamericana de Postgrado (AUIP).
The network brought together more than 50 researchers from 11 countries, promoting international scientific cooperation through recurring research seminars, specialist conferences, collaborative research initiatives, and special sessions at international mathematical meetings.
I have contributed to the organization or co-organization of nine international scientific events, delivered approximately 40 conference presentations and research contributions, and given approximately 30 research seminars at universities and research centres.
I have also promoted international academic mobility through the organization of research visits under the Giner de los Ríos Programme.
My scientific collaborations extend to researchers and institutions across approximately ten countries, providing a sustained international dimension to my research activity.
My research activity is closely connected with the supervision and training of students and early-career researchers.
In July 2026, I completed the co-supervision of a doctoral thesis in Mathematical Analysis and Applied Mathematics, entitled Orthogonal Polynomials and Moment Differential Equations, defended at the University of Alcalá and awarded the distinction Sobresaliente Cum Laude.
The thesis investigated moment differential operators, generalizations of classical polynomial differential equations, and advanced properties of orthogonal-polynomial families.
I have also supervised three Master's theses and twelve Bachelor's final projects, covering topics such as orthogonal polynomials, Support Vector Machines, Christoffel–Darboux kernels, artificial intelligence, statistical modelling, wavelet methods, signal processing, quantum algorithms, and quantum machine learning.
My university teaching experience spans four Spanish universities and one Portuguese university: Universidad a Distancia de Madrid, University of Alcalá, Technical University of Madrid, Universidad Carlos III de Madrid, and the University of Coimbra.
I have taught in Spanish, English, and Portuguese, across degree programmes in Mathematics, Engineering, Physics-related disciplines, Chemistry, Pharmacy, Forensic Science, Nursing, and Management.
My teaching experience includes Mathematical Analysis, Linear Algebra, Calculus, Statistics, Probability, Numerical Analysis, Optimization, and Computer Programming. At UDIMA, my current teaching activities focus on Mathematics and its applications within the framework of online higher education.
I have also held significant academic management and quality-assurance responsibilities.
From February 2020 to September 2022, I served as Academic Secretary of the Higher Polytechnic School of the University of Alcalá, participating in academic governance, institutional coordination, and administrative management across undergraduate and postgraduate engineering programmes.
I additionally served as a member of the DOCENTIA-UAH Teaching Evaluation Committee during two academic years and have received favourable institutional evaluations of my own university teaching activity.
I hold a Ph.D. in Mathematical Engineering from Universidad Carlos III de Madrid (2012), awarded Cum Laude with the European Doctorate distinction.
My doctoral dissertation, Analytic Properties of Krall-type and Sobolev-type Orthogonal Polynomials, was supervised by Professors Francisco Marcellán and Héctor Pijeira Cabrera.
My academic qualifications also include:
M.Sc. in Mathematical Engineering, Universidad Carlos III de Madrid (2009).
Technical Engineering Degree in Computer Systems, Universidad Nacional de Educación a Distancia — UNED (2005).
Degree in Physics, specializing in Fundamental Physics, Universidad Autónoma de Madrid (1996).
University Expert Diploma in Advanced Methods of Applied Statistics, UNED (2026).
My scientific training has been complemented by specialized studies in quantum computing, spectral methods, mathematical programming, signal processing, and computational methodologies.
Before consolidating my university academic career, I also worked in secondary education and software engineering, including professional responsibilities as a programmer analyst in the banking technology sector.
This combination of mathematical research, physical modelling, computational training, and practical software development continues to inform my approach to Applied Mathematics.
My current research agenda is directed towards the development of mathematical techniques that connect advanced analysis, orthogonal-polynomial theory, spectral methods, and modern computational learning models.
In particular, I aim to investigate the use of orthogonal-polynomial systems and their associated reproducing kernels in the mathematical foundations and practical implementation of Support Vector Machines, kernel-based learning algorithms, structured feature spaces, and Quantum Machine Learning.
A central objective is to develop mathematically interpretable approaches to nonlinear modelling, supervised classification, regression, and data analysis, drawing on analytical structures originating in approximation theory and orthogonality.
I am also interested in the interaction between these techniques and stochastic processes, quantum models, and scientific computing, particularly where spectral structure, mathematical regularity, and efficient computational representations play an important role.
My long-term goal is to consolidate an internationally connected research programme in Applied Mathematics, combining theoretical depth, interdisciplinary applications, scientific leadership, competitive research funding, and the training of new researchers.
Languages: Spanish (native), English (B2), Portuguese (B2).
Academic profile updated: October 2026.