MTM2011-28952-C02

Coordinator: Andrei Martínez Finkelshtein

Beginning: January 1, 2012

End: December 31, 2015

Summary:

This project combines both ambitious goals in fundamental research on orthogonal polynomials, of one and several variables, 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 computation), and technology (signal processing and diagnostic tools in ophthalmology, with applications in clinical practice).

Some of the problems to be tackled are:

Further development of new techniques, in particular, from complex analysis, operator theory, and the Riemann-Hilbert characterization, to the study of asymptotics and other properties of orthogonal polynomials, both of one and several variables.
Study of both classical stochastic processes (new random matrix models, non-intersecting diffusion processes, etc.) and quantum random walks by means of orthogonal polynomials approach, based on the results and methods obtained in the previous item.
Asymptotic analysis of rational approximants and of polynomial solutions of ODE.
Development of fast numerical algorithms related to orthogonal polynomials.
Study of information measures of families of special functions, with applications in quantum mechanics and medical imaging.
Development of methods of surface reconstruction and medical imaging with clinical applications in ophthalmology and human vision.

Structure:

Subproject MTM2011-28952-C02-01:

"Special functions and Approximation Theory: applications in Science and Technology" (SFAT-ST)

Subproject MTM2011-28952-C02-02:

"Multivariate orthogonal polynomials. Structural properties and applications" (POMPEYA)

Members:

Andrei Martínez-Finkelshtein (Universidad de Almería), principal investigator
Juan José Moreno Balcázar (Universidad de Almería)
Pedro Martínez González (Universidad de Almería)
Darío Ramos López (Universidad de Almería)
Leandro Moral Ledesema (Universidad de Zaragoza)
María José Cantero Medina (Universidad de Zaragoza)
Luis F. Velázquez Campoy (Universidad de Zaragoza)
Alejandro Zarzo Altarejos (Universidad Politécnica de Madrid)
A. B. J. Kuijlaars (Katholieke Universiteit Leuven, Belgium)