Profile (CV) of the research teaching staff

Velázquez Campoy, Luis Fernando
Department: Departamento de Matemática Aplicada
Field: Matemática Aplicada
Faculty: Escuela de Ingeniería y Arquitectura

Research Institute: INSTITUTO UNIVERSITARIO DE MATEMÁTICAS Y APLICACIONES (IUMA)

UNESCO codes
  • Teoría de la aproximación
  • Análisis armónico
  • Funciones especiales
  • Otras

Number of 6-year periods of research productivity evaluation
  • CNEAI research evaluation. 01/01/22
  • CNEAI research evaluation. 01/01/16
  • CNEAI research evaluation. 01/01/10
  • CNEAI research evaluation. 01/01/05
  • CNEAI research evaluation. 01/01/00
Academic position: Prof. Titular Univ.

Research interests
  • Mecánica cuántica
  • Análisis matemático

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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


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