Manuel Domínguez de la Iglesia
Instituto de Matemáticas
Universidad Nacional Autónoma de México
Mailing address:
Circuito Exterior, C.U.,
04510 México D.F., México.
Office: 218
Phone: (+52) 55 5622 4780
Fax: (+52) 55 5616 0348
Email: mdi29[at]im[dot]unam[dot]mx
Research interests
Approximation Theory, Special Functions, Matrixvalued Orthogonal Polynomials, Bispectral Problems, Matrix Analysis, RiemannHilbert problems, Fourier Analysis, Markov processes, Stochastic Calculus, Data Mining, Time Series Analysis, Principal Component Analysis.
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), 189207 (with F. A. Grünbaum).
.

Some examples of orthogonal matrix polynomials satisfying
odd order differential equations, J. Approx. Theory 150, No. 2, (2008), 153174 (with A. J. Durán).
.

Matrix valued orthogonal polynomials arising from group
representation theory and a family of quasibirthanddeath
processes, SIAM J. Matrix Anal. Applic. 30, No. 2 (2008), 741761 (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).
ArXiv

A note on the invariant distribution of a quasibirthanddeath process,
J. Phys. A: Math. Theor. 44 (2011) 135201 (9pp).
ArXiv

Some examples of matrixvalued orthogonal functions having a differential and an integral
operator as eigenfunctions,
J. Approx. Theory 163, No. 5, (2011), 663687.
ArXiv

Properties of matrix orthogonal polynomials via their RiemannHilbert characterization,
SIGMA 7 (2011), 098, 31 pages (with F. A. Grünbaum and A. MartínezFinkelshtein).

Spectral methods for bivariate Markov processes with diffusion and discrete components and a variant of the WrightFisher model,
J. Math. Anal. Appl. 393 (2012), 239255.
ArXiv

Principal dynamical components, Comm. Pure Appl. Math. 66 (2013), no. 1, 4882 (with Esteban Tabak).
ArXiv

Noncommutative Painlevé equations and Hermitetype matrix orthogonal polynomials, Commun. Math. Phys. 326 (2014), 559583. (with Mattia Cafasso).
ArXiv

Differential equations for discrete LaguerreSobolev orthogonal polynomials,
J. Approx. Theory (2015) (with A. J. Durán).
ArXiv

Constructing bispectral orthogonal polynomials from the classical discrete families of Charlier, Meixner and Krawtchouk,
Constr. Approx. 41 (2015), 4991 (with A. J. Durán).
ArXiv

Constructing KrallHahn orthogonal polynomials,
J. Math. Anal. Appl. 424 (2015), 361384. (with A. J. Durán).
ArXiv
Talks in conferences:

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 46, 2007.

New phenomena on examples of orthogonal matrix polynomials satisfying differential equations
. 2007 AMS Spring Western Section Meeting. Tucson, Arizona (USA), April 2223, 2007.

Second order differential operators having several families
of orthogonal matrix polynomials as eigenfunctions.
Special Functions, Information Theory and Mathematical Physics. Granada, España, September 1719, 2007.

Matrix valued orthogonal polynomials satisfying differential equations.
XX Congreso de Ecuaciones Diferenciales y Aplicaciones. X Congreso de Matemática Aplicada. Sevilla, September, 2428, 2007

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.

A family of quasibirthanddeath 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.

RiemannHilbert 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 matrixvalued orthogonal functions having a differential and an integral operator as eigenfunctions.
Congreso de la Real Sociedad Matemática Española 2011. Ávila, February 15, 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

A variant of the WrightFisher diffusion model coming from the theory of matrixvalued spherical functions.
1st Joint Conference of the Belgian, Royal Spanish and Luxembourg Mathematical Societies. Liège, Belgium, June 7th, 2012

Algebraic aspects of the RiemannHilbert problem for matrix orthogonal polynomials.
Orthogonal Polynomials and Special Functions: a Complex Analytic Perspective. Copenhague, Denmark, June 12th, 2012

Integral equations and representations of some Hermitetype families of orthogonal matrix polynomials.
Congreso de la Real Sociedad Matemática Española 2013. Santiago de Compostela, Spain, January, 2013.

Integral representations of some Hermite type matrixvalued kernels and noncommutative Painlevé equations.
Primer Encuentro de la Red de Polinomios Ortogonales y Teoría de Aproximación ORTHONET 2013. Logroño, Spain, February, 2013.

Noncommutative Painlevé equations and Hermitetype matrix orthogonal polynomials.
International Conference on Approximation Theory and Applications. Hong Kong, China, May 2024, 2013.

Constructing bispectral orthogonal polynomials from the classical families of Charlier, Meixner and Krawtchouk.
Constructive Functions 2014. Nashville, Tenneessee, USA, May 2630, 2014.

Differential equations for discrete LaguerreSobolev orthogonal polynomials.
IV Iberoamerican Workshop on Orthogonal Polynomials and Applications. Bogotá, Colombia, June 1720, 2014.

Aplicaciones de la ortogonalidad matricial a procesos estocásticos.
XLVII Congreso Nacional de la Sociedad Matemática Mexicana. Durango, México, October 2631, 2014.
Seminars:

Differential properties of some families of matrix valued
orthogonal polynomials and applications.
Courant Institute of
Mathematical Sciences. New York, March 11th, 2008.

Methods and applications of orthogonal matrix polynomials
satisfying differential equations.
Katholieke Universiteit Leuven. Leuven, June 11th, 2008.

The RiemannHilbert problem for matrixvalued orthogonal polynomials.
Katholieke Universiteit Leuven. Leuven, November 5th, 2008.

Properties of matrix orthogonal polynomials via their RiemannHilbert characterization.
Université d'Angers. Angers, France, April 17th, 2012.

Estudio espectral de procesos estocásticos bidimensionales. Componentes principales dinámicas.
Universidad Tecnologica de Panamá, Panamá, September 4th, 2012.

Principal Dynamical Components.
Instituto Nacional de Matemática Pura e Aplicada, IMPA, Brasil, May 15th, 2013.

RiemannHilbert characterization for matrix orthogonal polynomials.
City University of Hong Kong, China, May 28th, 2013.

Spectral methods for bivariate Markov processes.
City University of Hong Kong, China, May 30th, 2013.

Spectral methods for bivariate Markov processes.
Instituto de Matemáticas, UNAM, Sede CU, México, June 25th, 2013.

Spectral methods for bivariate Markov processes.
Instituto de Matemáticas, UNAM, Sede Cuernavaca, México, June 27th, 2013.

Como construir familias biespectrales de polinomios ortogonales a partir de familias clásicas.
Instituto de Matemáticas, UNAM, Sede CU, México, May 13th, 2014.

Aplicaciones de polinomios ortogonales matriciales.
Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas (IIMAS), UNAM, México, January 15th, 2015.

Sobre algunas extensiones de polinomios ortogonales y sus aplicaciones.
Instituto de Matemáticas, UNAM, Sede Cuernavaca, México, January 21st, 2015.
Posters:

A family of quasibirthanddeath processes coming from the
theory of matrix valued orthogonal polynomials.
3emes
Journees Approximation. Universite de Lille 1. Lille, May, 15,
2008.

A variant of the WrightFisher diffusion model coming from the thoery of matrixvalued spherical functions.
III Iberoamerican Workshop on Orthogonal Polynomials and Applications. Sao José do Rio Preto, Brazil, May, 2013.
PhD Thesis

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

Defense (spanish). February 21st 2008.