Coordinators: Andrei Martínez Finkelshtein and Juan José Moreno Balcázar

Beginning: Jan. 1, 2018

End: Dec. 31, 2021


This project combines both ambitious goals in fundamental research on orthogonal polynomials, special functions and their analytic and structural properties, with the applications of this knowledge in other branches of mathematics (stochastic processes, combinatorics, numerical analysis), physics (statistical physics, integrable systems, quantum mechanics, quantum random walks, quantum computation), and technology (signal processing and diagnostic tools in ophthalmology, with applications in clinical practice). Some of the problems to be tackled are:


  • Andrei Martínez-Finkelshtein (Universidad de Almería and Baylor University), principal investigator
  • Juan José Moreno Balcázar (Universidad de Almería), principal investigator
  • Pedro Martínez González (Universidad de Almería) 
  • Leandro Moral Ledesema (Universidad de Zaragoza)
  • María José Cantero Medina (Universidad de Zaragoza)
  • Luis F. Velázquez Campoy (Universidad de Zaragoza)
  • Lance L. Littlejohn (Baylor University, TX, USA)
  • Ana Belén Castaño Fernández (Universidad de Almería)
  • Juan Francisco Mañas Mañas (Universidad de Almería)

List of publications:


Preprints and papers in press:

  1. A. Martinez-Finkelshtein, G. Silva, Spectral Curves, Critical Measures and the Hermitian Random Matrix Model with External Source, in preparation.


  •  A. Martínez-Finkelshtein, L.L. Silva Ribeiro, A. S. Ranga, M. Tyaglov, Complementary Romanovski-Routh polynomials: From orthogonal polynomials on the unit circle to Coulomb wave functions, Proceedings of the AMS 147 (6) (2019), 2625–2640, Also preprint arXiv math.1806.02232.
  • A. Martinez-Finkelshtein, G. Silva, Critical measures for vector energy: asymptotics of non-diagonal multiple orthogonal polynomials for a cubic weight, Advances in Mathematics 349 (2019), 246-315. Also preprint ArXiv math:1805.01748.
  • A. Martínez-Finkelshtein, Brian Simanek, Barry Simon, Poncelet's Theorem, Paraorthogonal Polynomials and the Numerical Range of Compressed Multiplication Operators, Advances in Mathematics 349 (2019), 992-1035. Also preprint arXiv math.1810.13357.