Manuel Domínguez de la Iglesia

Mailing address:

Apartado de Correos 1160,

Sevilla E-41080, Spain.

Office #: 39.02 (junto a secretaría)

Telephone: (+34) 954559562; Fax: (+34) 954557972

E-mail: mdi29[at]us.es

Curriculum vitae

DOCENCIA

Research interests

Publications:

• Matrix valued orthogonal polynomials related to SU(N+1), their algebras of differential operators and the corresponding curves, Exp. Math. 16, No. 2, (2007), 189-207 (with F. A. Grünbaum). .

• Some examples of orthogonal matrix polynomials satisfying odd order differential equations, J. Approx. Theory 150, No. 2, (2008), 153-174 (with A. J. Durán). .

• Matrix valued orthogonal polynomials arising from group representation theory and a family of quasi-birth-and-death processes, SIAM J. Matrix Anal. Applic. 30, No. 2 (2008), 741-761 (with F. A. Grünbaum).

• Second order differential operators having several families of orthogonal matrix polynomials as eigenfunctions, Internat. Math. Research Notices, Vol. 2008, Article ID rnn084, 24 pages (with A. J. Durán).

• A note on the invariant distribution of a quasi-birth-and-death process, J. Phys. A: Math. Theor. 44 (2011) 135201 (9pp).

• Some examples of matrix-valued orthogonal functions having a differential and an integral operator as eigenfunctions, J. Approx. Theory 163, No. 5, (2011), 663--687.

• Properties of matrix orthogonal polynomials via their Riemann-Hilbert characterization, SIGMA 7 (2011), 098, 31 pages (with F. A. Grünbaum and A. Martínez-Finkelshtein).

• Principal dynamical components, accepted for publication in Communications on Pure and Applied Mathematics (with Esteban Tabak).

• Spectral methods for bivariate Markov processes with diffusion and discrete components and a variant of the Wright-Fisher model, submitted. See arXiv:1107.3733v1.

Talks:

• Matrix valued orthogonal polynomials related to SU(N+1), their algebras of differential operators and the corresponding curves. Recent trends in Contructive Approximation Theory. Universidad Carlos III de Madrid. September 1st, 2006.

• Some examples of orthogonal matrix polynomials satisfying odd order differential equations . 12th International Conference in Approximation Theory. San Antonio, Texas (USA). March 4-6, 2007.

• New phenomena on examples of orthogonal matrix polynomials satisfying differential equations . 2007 AMS Spring Western Section Meeting. Tucson, Arizona (USA), April 22-23, 2007.

• Second order differential operators having several families of orthogonal matrix polynomials as eigenfunctions. Special Functions, Information Theory and Mathematical Physics. Granada, Espańa, September 17-19, 2007.

• Matrix valued orthogonal polynomials satisfying differential equations. XX Congreso de Ecuaciones Diferenciales y Aplicaciones. X Congreso de Matemática Aplicada. Sevilla, September, 24-28, 2007

• Differential properties of some families of matrix valued orthogonal polynomials and applications. Random matrices and integrable systems working seminar. Courant Institute of Mathematical Sciences. New York, March, 11, 2008.

• The convex cone of weight matrices associated with a symmetric second order differential operator: some examples. Workshop on orthogonal polynomials and special functions. Katholieke Universiteit Leuven. Leuven, May, 20, 2008.

• Methods and applications of orthogonal matrix polynomials satisfying differential equations. Seminar Classical Analysis. Katholieke Universiteit Leuven. Leuven, June, 11, 2008.

• A family of quasi-birth-and-death processes coming from the theory of matrix valued orthogonal polynomials. International workshop on orthogonal polynomials and approximation theory. Universidad Carlos III de Madrid. Leganes, Madrid, September, 8, 2008.

• Riemann-Hilbert techniques in the theory of orthogonal matrix polynomials. XI Encuentros de Analisis Real y Complejo. Chinchon, Madrid, May 9, 2009.

• Methods and new phenomena of orthogonal matrix polynomials satisfying differential equations. 13th International Conference in Approximation Theory. San Antonio, Texas. March, 9, 2010.

• Differential properties of orthogonal matrix polynomials. International Congress of Mathematicians. Hyderabad, India. August, 21, 2010.

• Differential properties of orthogonal matrix polynomials. I Spanish Young Researchers Meeting in Mathematics. Universidad de Sevilla, Spain. September, 3, 2010.

• Some examples of matrix-valued orthogonal functions having a differential and an integral operator as eigenfunctions. Congreso de la Real Sociedad Matemática Espańola 2011. Ávila, February 1-5, 2011.

• Bivariate Markov processes and matrix orthogonality. 11th International Symposium on Orthogonal Polynomials, Special Functions and Applications. Universidad Carlos III de Madrid, September 1st, 2011

Posters:

• A family of quasi-birth-and-death processes coming from the theory of matrix valued orthogonal polynomials. 3emes Journees Approximation. Universite de Lille 1. Lille, May, 15, 2008.

PhD Thesis

• PhD thesis: Differential properties of families of matrix orthogonal polynomials and applications (spanish). Reviewed version (July 2008).
• Defense (spanish). February 21st 2008.