Manuel Domínguez de la Iglesia

Investigador Titular B

Instituto de Matemáticas

Universidad Nacional Autónoma de México



Mailing address:

Circuito Exterior, C.U.,

04510 Ciudad de México, México.


Office: 220

Phone: (+52) 55 5622 4780

Fax: (+52) 55 5616 0348

E-mail: mdi29[at]im[dot]unam[dot]mx


CV

Research interests

Approximation Theory, Special Functions, Orthogonal Polynomials, Matrix-valued Orthogonal Polynomials, Bispectral Problems, Matrix Analysis, Riemann-Hilbert problems, Fourier Analysis, Markov and stochastic processes, Quantum Markov chains.

Books:

  1. Orthogonal polynomials in the spectral analysis of Markov processes. Birth-death models and diffusion, Encyclopedia of Mathematics and its Applications 181, Cambridge University Press, 2022.

Articles:

  1. 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). .

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

  3. 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).

  4. 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

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

  6. 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. ArXiv

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

  8. Spectral methods for bivariate Markov processes with diffusion and discrete components and a variant of the Wright-Fisher model, J. Math. Anal. Appl. 393 (2012), 239-255. ArXiv

  9. Principal dynamical components, Comm. Pure Appl. Math. 66 (2013), no. 1, 48-82 (with Esteban Tabak). ArXiv

  10. Non-commutative Painlevé equations and Hermite-type matrix orthogonal polynomials, Commun. Math. Phys. 326 (2014), 559-583 (with Mattia Cafasso). ArXiv

  11. Differential equations for discrete Laguerre-Sobolev orthogonal polynomials, J. Approx. Theory 195 (2015), 70-88 (with A. J. Durán). ArXiv

  12. Constructing bispectral orthogonal polynomials from the classical discrete families of Charlier, Meixner and Krawtchouk, Constr. Approx. 41 (2015), 49-91 (with A. J. Durán). ArXiv

  13. Constructing Krall-Hahn orthogonal polynomials, J. Math. Anal. Appl. 424 (2015), 361-384 (with A. J. Durán). ArXiv

  14. Differential equations for discrete Jacobi-Sobolev orthogonal polynomials, J. Spectral Theory 8 (2018), 191-234 (with A. J. Durán). ArXiv

  15. Some bivariate stochastic models arising from group representation theory, Stoch. Proc. Appl. 128 (2018), 3300-3326 (with Pablo Román). ArXiv

  16. The Toda and Painlevé systems associated with semiclassical matrix-valued orthogonal polynomials of Laguerre type, SIGMA 14 (2018), 076, 17 pages (con M. Cafasso). ArXiv

  17. On difference operators for symmetric Krall-Hahn polynomials, Integral Transforms and Special Functions 29 (2018), 699-718 (with A. J. Durán). ArXiv

  18. Stochastic LU factorizations, Darboux transformations and urn models, J. Appl. Prob. 55 (2018), 862-886 (with F. A. Grünbaum). ArXiv

  19. Stochastic Darboux transformations for quasi-birth-and-death processes and urn models, J. Math. Anal. Appl. 478 (2019), 634-654 (with F. A. Grünbaum). ArXiv

  20. Bispectral Laguerre type polynomials, Integral Transforms and Special Functions 31 (2020), 133-151(with A. J. Durán). ArXiv

  21. The spectral matrices associated with the stochastic Darboux transformations of random walks on the integers, J. Approx. Theory 258 (2020) 105458, 32 pp. (with C. Juarez). ArXiv

  22. Quasi-birth-and-death processes and multivariate orthogonal polynomials, J. Math. Anal. Appl. 499 (2021), 125029, 33 pp. (with L. Fernández). ArXiv

  23. Absorbing-reflecting factorizations for birth-death chains on the integers and their Darboux transformations, J. Approx. Theory 266 (2021) 105583, 27 pp. (with C. Juarez). ArXiv

  24. Bispectral Jacobi type polynomials, Adv. Appl. Math. 136 (2022), 102322, 35 pp. (with A. J. Durán). ArXiv

  25. An urn model for the Jacobi-Piñeiro polynomials, Proc. Amer. Math. Soc. 150 (2022), 3613-3625 (with F. A. Grünbaum). ArXiv

  26. Spectral analysis of bilateral birth-death processes: some new explicit examples, Adv. Appl. Prob. 54 (2022), 1193-1221. ArXiv

  27. Quantum Markov chains on the line: matrix orthogonal polynomials, spectral measures and their statistics, Quantum Inf Process 22 (2023), 60, 57 pp . (with C. Lardizabal and N. Loebens). ArXiv

  28. Birth-death chains on a spider: spectral analysis and reflecting-absorbing factorization, J. Math. Anal. Appl. 517 (2023), 126624, 20 pp. (with C. Juarez). ArXiv

  29. QBD processes associated with Jacobi-Koornwinder bivariate polynomials and urn models, Mediterr. J. Math. 20 (2023), no.6, Paper No. 290, 23 pp. (with L. Fernández). ArXiv

  30. The bilateral birth-death chain generated by the associated Jacobi polynomials, Stud. Appl. Math. 151 (2023) 616-642 (with C. Juarez). ArXiv

Talks in conferences:

  1. 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 1, 2006.

  2. 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.

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

  4. Second order differential operators having several families of orthogonal matrix polynomials as eigenfunctions. Special Functions, Information Theory and Mathematical Physics. Granada, Spain, September 18, 2007.

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

  6. 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, Belgium, May 20, 2008.

  7. 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. Leganés, Madrid, September 8, 2008.

  8. Riemann-Hilbert techniques in the theory of orthogonal matrix polynomials. XI Encuentros de Análisis Real y Complejo. Chinchón, Madrid, Spain, May 9, 2009.

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

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

  11. Differential properties of orthogonal matrix polynomials. I Encuentro Nacional de Jóvenes Investigadores en Matemáticas. Sevilla, Spain. September 3, 2010.

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

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

  14. A variant of the Wright-Fisher diffusion model coming from the theory of matrix-valued spherical functions. 1st Joint Conference of the Belgian, Royal Spanish and Luxembourg Mathematical Societies. Liège, Belgium, Junio 7, 2012.

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

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

  17. Integral representations of some Hermite type matrix-valued kernels and non-commutative Painlevé equations. Primer Encuentro de la Red de Polinomios Ortogonales y Teoría de Aproximación ORTHONET 2013. Logroño, Spain, February, 2013.

  18. Non-commutative Painlevé equations and Hermite-type matrix orthogonal polynomials. International Conference on Approximation Theory and Applications. Hong Kong, China, May 20-24, 2013.

  19. Constructing bispectral orthogonal polynomials from the classical families of Charlier, Meixner and Krawtchouk. Constructive Functions 2014. Nashville, Tenneessee (USA), May 26-30, 2014.

  20. Differential equations for discrete Laguerre-Sobolev orthogonal polynomials. IV Iberoamerican Workshop on Orthogonal Polynomials and Applications. Bogotá, Colombia, June 17-20, 2014.

  21. Aplicaciones de la ortogonalidad matricial a procesos estocásticos. XLVII Congreso Nacional de la Sociedad Matemática Mexicana. Durango, México, October 26-31, 2014.

  22. Differential equations for discrete Sobolev orthogonal polynomials. 13th International Symposium on Orthogonal Polynomials, Special Functions and Applications (OPSFA-13), National Institute of Standards and Technology, Gaithersburg, Maryland (USA), June 1-5, 2015.

  23. Krall-Hahn orthogonal polynomials. Workshop on Orthogonal and Multiple Orthogonal Polynomials, BIRS-CMO, Oaxaca (México), August 9-14, 2015.

  24. Approximation of matrix functions via orthogonal matrix polynomials. First Joint International Meeting of the Israel Mathematical Union and the Mexican Mathematical Society, Oaxaca (México), September 7-11, 2015.

  25. Two stochastic models related with an example coming from group representation theory. XII International Conference in Approximation and Optimization in the Caribbean, Universidad de La Habana (Cuba), June 5-10, 2016.

  26. Some recent developments about birth-and-death models and orthogonal polynomials. VI Iberoamerican Workshop on Orthogonal Polynomials and Applications, Uberaba, May 9-12, 2017.

  27. Factorization of stochastic Jacobi matrices into two stochastic factors and Darboux transformations. 14th International Symposium on Orthogonal Polynomials, Special Functions and Applications (OPSFA 14), Canterbury, July 3-7, 2017.

  28. Darboux transformations for quasi-birth-and-death processes. VII Iberoamerican Workshop on Orthogonal Polynomials and Applications, Leganés, Madrid, July 3-6, 2018.

  29. Bispectral Laguerre and Jacobi type polynomials. 15th International Symposium on Orthogonal Polynomials, Special Functions and Applications (OPSFA 15), Hagenberg, Austria, July 22-26, 2019.

  30. The spectral matrices associated with the stochastic Darboux transformations of random walks on the integers. Bath-UNAM-CIMAT Meeting XVI (BUC XVI), Ciudad de México, September 2-6, 2019.

  31. Bispectrality of Laguerre and Jacobi type polynomials. Operator Theory, Analysis and Mathematical Physics (OTAMP 2020), Ciudad de México, January 8-14, 2020.

  32. Absorbing-reflecting factorizations for birth-death chains on the integers and their Darboux transformation. V Encuentro Conjunto de la Real Sociedad Matemática Española (RSME) y la Sociedad Matemática Mexicana (SMM), Guanajuato, México, June 14-18, 2021 (online).

  33. Stochastic factorizations of birth-death chains and Darboux transformations. Mathematical Congress of the Americas, Buenos Aires, Argentina, July 12-23, 2021 (online).

  34. Discrete Krall polynomials. Baylor Analysis Fest, Waco, TX, USA, May 24, 2022.

  35. Bispectral Jacobi type polynomials. 16th International Symposium on Orthogonal Polynomials, Special Functions and Applications (OPSFA 16), Montreal, Canada, June 17, 2022 (online).

Seminars:

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

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

  3. The Riemann-Hilbert problem for matrix-valued orthogonal polynomials. Katholieke Universiteit Leuven. Leuven, November 5, 2008.

  4. Properties of matrix orthogonal polynomials via their Riemann-Hilbert characterization. Université d'Angers. Angers, France, April 17, 2012.

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

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

  7. Riemann-Hilbert characterization for matrix orthogonal polynomials. City University of Hong Kong, China, May 28, 2013.

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

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

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

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

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

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

  14. Representación espectral de caminatas aleatorias. CIMAT, Guanajuato, México, April 6, 2015.

  15. Polinomios ortogonales matriciales que verifican ecuaciones diferenciales. Universidad Autónoma Metropolitana, Iztapalapa, Ciudad de México, February 25, 2016.

  16. Algunos ejemplos de análisis espectral de procesos de Markov bidimensionales. Seminario de Probabilidad y Procesos Estocásticos, IMATE, UNAM, Ciudad de México, September 20, 2016.

  17. Teoría de la aproximación para funciones matriciales. Instituto Tecnológico Autónomo de México, Ciudad de México, October 7, 2016.

  18. Algunas aplicaciones de polinomios ortogonales. Universidad Autónoma de Aguascalientes, Aguascalientes, March 17, 2017.

  19. Nuevos métodos para el análisis espectral de caminatas aleatorias. Universidad de Colima, Colima, November 17, 2017.

  20. Transformaciones de Darboux para caminatas aleatorias. Centro de Ciencias Matemáticas, UNAM, Morelia, March 8, 2018.

  21. Biespectralidad de polinomios definidos mediante un determinante de tipo Casorati. II Escuela de Análisis Matemático, IMATE-UNAM, August 1, 2018.

  22. Historia y aplicaciones de polinomios ortogonales. Hablando de Matemáticas, IMATE-UNAM, March 21, 2019.

  23. Caminatas aleatorias y polinomios ortogonales. CINVESTAV, Ciudad de México, May 22, 2019.

  24. Matrices espectrales asociadas a transformaciones de Darboux estocásticas de caminatas aleatorias en los enteros. Coloquio del Instituto de Matemáticas, UNAM, Sede CU, México, August 13, 2019.

  25. Modelos de urnas para polinomios de tipo Jacobi. Seminario Grupo GOYA, Granada, Spain, May 28, 2021 (online).

  26. Historia y aplicaciones de polinomios ortogonales. Seminario Iberoamericano de Análisis Matemático y Matemática Aplicada, February 11, 2022 (online).

Posters:

  1. 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.

  2. A variant of the Wright-Fisher diffusion model coming from the thoery of matrix-valued spherical functions. III Iberoamerican Workshop on Orthogonal Polynomials and Applications. Sao José do Rio Preto, Brasil, May, 2013.

PhD Thesis