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Although my research career starts with a PhD in theoretical physics, applied mathematics has been protagonist of a good deal of it. My collaboration with M.J. Cantero and L. Moral soon led to new results on orthogonal polynomials (OP) which brought us international recognition: the CMV matrices, revulsive in OP theory, uncovered fundamental links with other fields (operator theory, integrable systems, matrix models, solid state physics,…) and broadening my interests to interdisciplinary research lines.
These years have witnessed a boom in quantum information technologies. Quantum walks (QW), quantum version of random walks, emerged as key platforms for quantum information processing. In collaboration with F. Grünbaum (UC Berkeley), the discoverers of CMV matrices uncovered their fruitful connections with QW (CGMV method), attracting collaborations of internationally renowned figures in mathematics (J. Bourgain, Fields Medal 1994) and quantum information (R. Werner, International Quantum Communication Award 2014). This gave rise to quantum dynamical results, triggered pay-offs to mathematics (OP and harmonic analysis) and paved the way to novel approaches to quantum Markov chains and topological quantum phases (2016 Noble Prize).
This has placed me at a crossroads, challenged by symbiotic relations among different areas of mathematics and quantum physics. My current interests cover a wide variety of disciplines around approximation theory, their matrix and spectral approach, links with harmonic analysis and connections with burning topics in classical and quantum random systems.
This has fostered strong partnerships with researchers from institutions around the world, e.g., IAS Princeton (J. Bourgain, passed away), Leibniz U Hannover (R. Werner), U Copenhagen (A. Werner), UC Berkeley (F. Grünbaum), UFRGS Brazil (C. Lardizabal), U Montreal (L. Vinet), Yokohama National U (N. Konno), Shangai Jiao Tong U (T. Ratiu). These relationships have been stimulated by research stays (U Copenhagen, CRM Montreal, Shanghai Jiao Tong U, IMPA Brazil, Leibniz U Hannover, UC Berkeley, Caltech, NTNU Norway, U Patras) and organization of international workshops at CRM Montreal, BIRS Canadá and Centro de Ciencias de Benasque.
I have been reviewer for indexed journals in mathematics and physics (J. Approx. Theory, Appl. Math. Let., IMRN, Constr. Approx., Linear Alg. Appl., J. Comp. Appl. Math., Cent. Eur. J. Math., Adv. Dif. Eq., J. Math. Pures Appl., Acta Appl. Math., Quant. Inf. Proc., Quant. Inf. Comp., J. Phys. A: Math. Theor.), ANEP expert for evaluation of national projects and external reviewer for BIRS program.
I was supervisor of a postdoctoral researcher from U Patras (Greece), advisor of a Master’s Degree at U Zaragoza, and an Undergraduate Thesis at U Patras headed in 2006 within the Socrates-Erasmus Program was the origin of my position as contact for the bilateral agreement between U Zaragoza and U Patras. I have been principal investigator of an AEI project on OP and interdisciplinary applications, and of the research group “Análisis y Física Matemática” funded by Gobierno de Aragón, which brings together around 30 researchers in analysis, probability and statistics, special functions and mathematical physics.
Sexennial periods: 5 (2016-2022 last one)
WEB of SCIENCE Citations: 1.012 Citatons/year (last 5 years): 66,4 Publications: 37 (Q1-22) h-index: 14
- Research sexennial periods: 5 (2016-2022 last one)
- Publications: 49
WEB of SCIENCE INDICATORS
- Citations: 1.012
- Citations without self-citations: 937
- Citations/year (last 5 years): 66,4
- Publications indexed by Web of Science: 37
- Publications Q1: 22
- H-index: 14
Journal articles
- Cantero, M. J.; Moral, L.; Velázquez, L. Wall Polynomials on the Real Line: a classical approach to OPRL Khrushchev’s formula. CONSTRUCTIVE APPROXIMATION. 2022. DOI: 10.1007/s00365-022-09583-4
- Cedzich C.; Geib T.; Grünbaum F.A.; Velázquez Campoy, L. F.; Werner A.H.; Werner R.F. Quantum Walks: Schur Functions Meet Symmetry Protected Topological Phases. COMMUNICATIONS IN MATHEMATICAL PHYSICS. 2022. DOI: 10.1007/s00220-021-04284-8
- Lardizabal, C.F.; Velázquez, L. Mean hitting time formula for positive maps. LINEAR ALGEBRA AND ITS APPLICATIONS. 2022. DOI: 10.1016/j.laa.2022.06.011
- Grünbaum, F. A.; Velázquez, L.; Wilkening, J. Occupation Time for Classical and Quantum Walks. OPERATOR THEORY. 2021. DOI: 10.1007/978-3-030-75425-9_11
- Cantero, M.J.; Marcellán, F.; Moral, L.; Velázquez, L. Darboux Transformations for Orthogonal Polynomials on the Real Line and on the Unit Circle. SEMA SIMAI SPRINGER SERIES. 2021. DOI: 10.1007/978-3-030-56190-1_3
- Cantero, M.J.; Marcellán, F.; Moral, L.; Velázquez, L. A CMV connection between orthogonal polynomials on the unit circle and the real line. JOURNAL OF APPROXIMATION THEORY. 2021. DOI: 10.1016/j.jat.2021.105579
- Grünbaum, F. A.; Lardizabal, C. F.; Velázquez, L. Quantum Markov Chains: Recurrence, Schur Functions and Splitting Rules. ANNALES HENRI POINCARE. 2020. DOI: 10.1007/s00023-019-00863-7
- Cedzich, C.; Geib, T.; Stahl, C.; Velazquez, L.; Werner, A.H.; Werner, R.F. Complete homotopy invariants for translation invariant symmetric quantum walks on a chain. QUANTUM. 2018. DOI: 10.22331/q-2018-09-24-95
- Grunbaum, F.A.; Velazquez, L. A generalization of Schur functions: Applications to Nevanlinna functions, orthogonal polynomials, random walks and unitary and open quantum walks. ADVANCES IN MATHEMATICS. 2018. DOI: 10.1016/j.aim.2017.12.014
- Grunbaum, F.A.; Velazquez, L. The CMV Bispectral Problem (vol 9, pg 079, 2013). INTERNATIONAL MATHEMATICS RESEARCH NOTICES. 2017. DOI: 10.1093/imrn/rnw228
- Cedzich, C.; Geib, T.; Grünbaum, F.A.; Stahl, C.; Velázquez, L.; Werner, A.H.; Werner, R.F. The Topological Classification of One-Dimensional Symmetric Quantum Walks. ANNALES HENRI POINCARE. 2017. DOI: 10.1007/s00023-017-0630-x
- Grünbaum, F.A.; Velázquez, L. The CMV bispectral problem. INTERNATIONAL MATHEMATICS RESEARCH NOTICES. 2017. DOI: 10.1093/imrn/rnw186
- Cantero, M. J.; Marcellán, F.; Moral, L.; Velázquez, L. Darboux transformations for CMV matrices. ADVANCES IN MATHEMATICS. 2016. DOI: 10.1016/j.aim.2016.03.042
- Cedzich, C.; Grünbaum, F. A.; Stahl, C.; Velázquez, L.; Werner, A. H.; Werner, R. F. Bulk-edge correspondence of one-dimensional quantum walks. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL. 2016. DOI: 10.1088/1751-8113/49/21/21LT01
- Cedzich, C.; Grünbaum, F. A.; Velázquez, L.; Werner, A. H.; Werner, R. F. A Quantum Dynamical Approach to Matrix Khrushchev's Formulas. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS. 2016. DOI: 10.1002/cpa.21579
- Petropoulou, E. N.; Velázquez, L. Self-adjointness of unbounded tridiagonal operators and spectra of their finite truncations. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. 2014. DOI: 10.1016/j.jmaa.2014.05.077
- Bourgain, J.; Grünbaum, F. A.; Velázquez, L.; Wilkening, J. Quantum Recurrence of a Subspace and Operator-Valued Schur Functions. COMMUNICATIONS IN MATHEMATICAL PHYSICS. 2014. DOI: 10.1007/s00220-014-1929-9
- Grünbaum, F. A.;Velázquez, L.;Werner, A. H.;Werner, R. F. Recurrence for Discrete Time Unitary Evolutions. COMMUNICATIONS IN MATHEMATICAL PHYSICS. 2013. DOI: 10.1007/s00220-012-1645-2
- Olmos,B.;González-Férez,R.;Lesanovsky,I.;Velázquez,L. Universal time evolution of a Rydberg lattice gas with perfect blockade. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL. 2012. DOI: 10.1088/1751-8113/45/32/325301
- Cantero,M. J.;Grünbaum,F. A.;Moral,L.;Velázquez,L. One-dimensional quantum walks with one defect. REVIEWS IN MATHEMATICAL PHYSICS. 2012. DOI: 10.1142/S0129055X1250002X
- Cantero, M.; Moral, L.; Velázquez, L. Spectral transformations of hermitian linear functionals. CONTEMPORARY MATHEMATICS - AMERICAN MATHEMATICAL SOCIETY. 2012. DOI: 10.1090/conm/578/11475
- Cantero, M. J.;Grünbaum, F. A.;Moral, L.;Velázquez, L. The CGMV method for quantum walks. QUANTUM INFORMATION PROCESSING. 2012. DOI: 10.1007/s11128-012-0448-x
- Cantero,M. J.;Moral,L.;Velázquez,L. Direct and inverse polynomial perturbations of hermitian linear functionals. JOURNAL OF APPROXIMATION THEORY. 2011. DOI: 10.1016/j.jat.2011.02.014
- Deckers, K.;Cantero, M. J.;Moral, L. ;Velázquez, L. An extension of the associated rational functions on the unit circle. JOURNAL OF APPROXIMATION THEORY. 2011
- Cantero, M. -.;Alberto Grünbaum, F.;Moral, L. ;Velázquez, L. Matrix-valued Szego{double acute} polynomials and quantum random walks. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS. 2010
- Njastad, O.; Velazquez,L. Wall Rational Functions and Khrushchev's Formula for Orthogonal Rational Functions. CONSTRUCTIVE APPROXIMATION. 2009
- Velazquez, L. Spectral Methods for Orthogonal Rational Functions. JOURNAL OF FUNCTIONAL ANALYSIS. 2008
- Cantero, M. J.;Moral,L.;Velazquez,L. Matrix Orthogonal Polynomials Whose Derivatives are also Orthogonal. JOURNAL OF APPROXIMATION THEORY. 2007
- Cantero,M. J.;Moral,L.;Velazquez,L. Measures on the unit circle and unitary truncations of unitary operators. JOURNAL OF APPROXIMATION THEORY. 2006
- Siafarikas, P. D.;Stabolas, I. D.;Velazquez, L. Differential Inequalities of Functions Involving the Lowest Zero of Some Associated Orthogonal Q-Polynomials. INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS. 2005
- Cantero, M. J.; Moral, L.; Velázquez, L. Differential properties of matrix orthogonal polynomials. JOURNAL OF CONCRETE AND APPLICABLE MATHEMATICS. 2005
- Cantero, M. J.;Moral, L.;Velazquez, L. Minimal Representations of Unitary Operators and Orthogonal Polynomials on the Unit Circle. LINEAR ALGEBRA AND ITS APPLICATIONS. 2005
- Cantero, M. J.;Moral, L.;Velazquez, L. Five-Diagonal Matrices and Zeros of Orthogonal Polynomials on the Unit Circle. LINEAR ALGEBRA AND ITS APPLICATIONS. 2003
- Cantero, M. J.;Ferrer, M. P.;Moral, L.;Velazquez, L. A Connection Between Orthogonal Polynomials on the Unit Circle and Matrix Orthogonal Polynomials on the Real Line. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. 2003
- Cantero, M. J.; Moral, L.; Velázquez, L. Measures and para-orthogonal polynomials on the unit circle. EAST JOURNAL ON APPROXIMATIONS. 2002
- Cortes, J.L.; Gamboa, J.; Velazquez, L. A Nambu-Jona-Lasinio like model from QCD at low energies. PHYSICS LETTERS B. 1998. DOI: 10.1016/S0370-2693(98)00694-7
- Gamboa Rios, Jorge F. ; Cortés Azcoiti, José L.; Velázquez Campoy, Luis F. Estadísticas fraccionarias y topología. INVESTIGACIÓN Y CIENCIA. 1996
- Cortes, J. L.; Rivas, E.; Velazquez, L. Extended dualization: A method for the bosonization of anomalous fermion systems in arbitrary dimension. PHYSICAL REVIEW. D. PARTICLES AND FIELDS. 1996. DOI: 10.1103/physrevd.53.5952
- Cortes, J. L.; Gamboa, J.; Velazquez, L. Electromagnetic interaction of anyons in Nonrelativistic Quantum Field Theory. INTERNATIONAL JOURNAL OF MODERN PHYSICS A. 1994. DOI: 10.1142/s0217751x94000431
- Cortes, J. L.; Gamboa, J.; Velazquez, L. A U(1) Gauge Theory for Anyons. NUCLEAR PHYSICS B. 1993. DOI: 10.1016/0550-3213(93)90520-y
- Cortes, J. L.; Gamboa, J.; Velazquez, L. Second Order Formalism for Lattice Fermions. NUCLEAR PHYSICS B - PROCEEDINGS SUPPLEMENTS. 1993. DOI: 10.1016/0920-5632(93)90289-I
- Cortes, J. L.; Gamboa, J.; Velazquez, L. Second Order Formalism for Fermions. PHYSICS LETTERS B. 1993. DOI: 10.1016/0370-2693(93)91198-v
- Cortes, J. L.; Plyushchay, M. S.; Velazquez, L. A Pseudoclassical Model for the Massive Dirac Particle in D-Dimensions. PHYSICS LETTERS B. 1993. DOI: 10.1016/0370-2693(93)91133-8
- Cortes, J. L.;Gamboa, J.;Velazquez, L. Electromagnetic-Interaction of Anyons. PHYSICS LETTERS B. 1992
- Cortés, J.L.; Gamboa, J.; Velázquez, L. Electromagnetic interaction of anyons. PHYSICS LETTERS B. 1992. DOI: 10.1016/0370-2693(92)90165-z
Projects
- E48_23R: Análisis y física matemática. 01/01/23 - 31/12/25
- PID2021-124472NB-I00 NUEVAS TENDENCIAS EN APROXIMACION CONSTRUCTIVA: TEORIA Y APLICACIONES. 01/09/22 - 31/08/25
- E48_20R: Análisis Y Física Matemática. 01/01/20 - 31/12/22
- UAL18-FQM-B025-A POLINOMIOS ORTOGONALES: MÉTODOS ANALÍTICOS Y FUNCIONALES, APLICACIONES CLÁSICAS Y
CUÁNTICAS. 01/01/19 - 31/12/22
- MTM2017-89941-P APROXIMACION CONSTRUCTIVA: ANALISIS, ALGORITMOS Y APLICACIONES. 01/01/18 - 31/12/21
- GRUPO DE REFERENCIA ANÁLISIS MATEMÁTICO Y APLICACIONES. 01/01/17 - 31/12/19
- GRUPO CONSOLIDADO E64 ANÁLISIS MATEMÁTICO Y APLICACIONES. 01/01/16 - 31/12/16
- GRUPO CONSOLIDADO E64 ANÁLISIS MATEMÁTICO Y APLICACIONES. 01/01/15 - 31/12/15
- MTM2014-53963-P APROXIMACION Y ORTOGONALIDAD: DE LA TEORIA A LAS APLICACIONES. 01/01/15 - 31/12/17
- GRUPO CONSOLIDADO E64 ANÁLISIS MATEMÁTICO Y APLICACIONES. 01/01/14 - 31/12/14
- GRUPO CONSOLIDADO E64 ANÁLISIS MATEMÁTICO Y APLICACIONES. 01/01/13 - 31/12/13
- MTM2011-28952-C02-01 FUNCIONES ESPECIALES Y TEORIA DE APROXIMACION. APLICACIONES EN CIENCIA Y TECNOLOGIA. 01/01/12 - 31/12/14
- GRUPO CONSOLIDADO E64 ANALISIS MATEMATICO Y APLICACIONES. 01/01/11 - 31/12/12
- SUB. NO SUJETA A CONV. 2011. INTERNATIONAL INTERDISCIPLINARY WORKSHOP "QUANTUM AND CLASSICAL RANDOM PROCESSES". 01/01/11 - 14/11/11
- MTM2008-06689-C02-01 POLINOMIOS ORTOGONALES: TEORIA Y APLICACIONES EN LAS MATEMATICAS, LA FISICA Y LA TECNOLOGIA. 01/01/09 - 31/12/11
- GRUPO EXCELENTE E64 ANALISIS MATEMATICO Y APLICACIONES. 01/01/08 - 31/12/10
- VI MOVILIDAD 2007. 01/01/08 - 31/12/08
- MTM2005-08648-C02-01. FUNCIONES ESPECIALES Y POLINOMIOS ORTOGONALES. APROXIMACION CONSTRUCTIVA Y APLICACIONES. 31/12/05 - 30/12/08
- GRUPO CONSOLIDADO E64 ANALISIS MATEMATICO Y APLICACIONES. 01/01/05 - 31/12/07
- IBE2004B-CIE-07. OPERADORES UNITARIOS, POLINOMIOS ORTOGONALES Y APROXIMACIÓN RACIONAL. 01/01/05 - 31/12/06
- IBE2002-CIEN-07. TEORIA ESPECTRAL Y POLINOMIOS ORTOGONALES EN LA CIRCUNFERENCIA UNIDAD. 01/01/03 - 31/12/04
- PB98-1615 FUNCIONES SEMIORTOGONALES Y POLINOMIOS ORTOGONALES SOBRE LA CIR- CUNFERENCIA UNIDAD. 30/12/99 - 30/12/02
- UNA NUEVA CLASE DE ORTOGONALIDAD. 01/01/99 - 30/12/99
- UZ97-CIE-10 UNA NUEVA CLASE DE ORTOGONALIDAD. 02/12/97 - 02/12/98
- AEN97-1680 ASPECTOS NO PERTURBATIVOS DE FISICA CUANTICA DE CAMPOS. 01/10/97 - 30/09/00
- AEN96-1670. NUEVOS EFECTOS EN TEORIA CUANTICA DE CAMPOS. 09/09/96 - 09/09/97
Contracts
- Análisis Y Física Matemática (Retorno UZ). 17/11/08 - 31/12/28
Supervision of master's theses
- Teoría de polinomios ortogonales y teoría de operadores. Universidad de Zaragoza. Sobresaliente. 20/09/12
Participation in conferences
- Dos Días de Polinomios Ortogonales y Funciones Especiales 2023. Participativo - Ponencia invitada/ Keynote. Medidas de Khrushchev en la recta real. Almería. 14/12/23
- 16th International Symposium on Orthogonal Polynomials, Special Functions and Applications. Participativo - Plenaria. Orthogonal polynomials & quantum walks: Schur connections. Montreal. 13/06/22
- 9th International Conference on Quantum Walks and Quantum Simulation. Participativo - Ponencia invitada/ Keynote. Quantum walks: return functions & topological phases. Marsella. 20/01/20
- Algebraic Graph Theory & Quantum Walks. Participativo - Ponencia invitada/ Keynote. Recurrence & splitting in quantum walks. Waterloo. 23/04/18
- Classical and Quantum Physics: Geometry, Dynamics and Control. Participativo - Ponencia invitada/ Keynote. Recurrence and topological pohases in quantum walks. Madrid. 05/03/18
- 6th Workshop of Quantum Simulation and Quantum Walks. Participativo - Ponencia invitada/ Keynote. From quantum recurrence to topological phases in quantum walks. Praga. 17/11/16
- ORTHONET 2016. Participativo - Ponencia invitada/ Keynote. Polinomios ortogonales y "quantum walks": caminos de ida y vuelta. Albarracín (Teruel). 06/05/16
- Quantum Physics: Foundations and Applications. Participativo - Ponencia invitada/ Keynote. Quantum recurrence. Stellenbosch. 03/02/15
- International Workshop on Noncommutative Analysis and Its Future Prospects Participativo - Ponencia invitada/ Keynote. Quantum recurrence and Schur functions. Sapporo. 05/08/13
- International Conference on Differential Equations, Difference Equations and Special Functions. Participativo - Ponencia invitada/ Keynote. Orthogonal polynomials, random walks and recurrence. Patras. 03/09/12
Research stays
- Department of Mathematical Sciences, University of Copenhagen Copenhague. Dinamarca. 01/03/26 - 07/03/26
- Centre de Recherches Mathématiques, Université de Montréal. Montreal. Canadá. 25/07/22 - 19/08/22
- School of Mathematical Sciences, Shanghai Jiao Tong University Shanghai. China. 04/03/19 - 30/03/19
- Department of Mathematics, University of California, Berkeley. Berkeley, CA. Estados Unidos de América. 16/04/10 - 15/05/10
- Department of Mathematics, University of California, Berkeley. Berkeley, CA. Estados Unidos de América. 13/04/09 - 22/05/09
- Division of Physics, Mathematics and Astronomy, California Institute of Technology. Pasadena, CA. Estados Unidos de América. 02/04/08 - 30/05/08
- Departamento de Análisis Matemático, Universidad de La Laguna. Tenerife. España. 02/06/07 - 30/06/07
- Department of Mathematical Sciences, Norwegian University od Science and Technology. Trondheim. Noruega. 18/04/05 - 31/07/05
- Department of Mathematics, University of Patras. Patras. Grecia. 17/04/03 - 31/05/03
- Department of Mathematics, University of Patras. Patras. Grecia. 25/02/02 - 24/05/02
- Department of Mathematics, University of Patras. Patras. Grecia. 26/02/01 - 25/05/01
- Department of Mathematics, University of Patras. Patras. Grecia. 17/03/00 - 17/04/00
- Theory Division, CERN. Ginebra. Suiza. 14/10/90 - 25/11/90
Organization of R&D activities
- Graph Theory, Algebraic Combinatorics and Mathematical Physics. 25/07/22 - 19/08/22
- Quantum Walks and Information Tasks. 21/04/19 - 26/04/19
- Quantum and Classical Random Processes. 20/05/11 - 26/05/11
Research evaluation activities
- Evaluador de propuestas científicas para BIRS. BIRS external reviewer Canadá. 22/10/19 - 20/11/19
- Experto de la Agencia Estatal de Investigación Experto ANEP. España. 05/10/15 - 13/12/21
UNIZAR teaching of the last six courses
- Algebra. Bachelor Degree in Mechanical Engineering. During academic year 2025-26
- Algebra. Bachelor Degree in Electronics and Automation Engineering. During academic year 2025-26
- Algebra. Bachelor Degree in Chemical Engineering. During academic year 2025-26
- Mathematics II. Bachelor's Degree in Industrial Engineering Technology. From the 2020-21 course to the 2025-26 course
- Mathematics II. Bachelor's Degree in Mechanical Engineering. From the 2020-21 course to the 2024-25 course
- Mathematics. Degree in Chemistry. During academic year 2022-23
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