Curso 2007-2008:

Viernes, 4 de julio de 2008.
Lugar: M3, Facultad de Ciencias, Universidad de Granada. 
Sesión: 12.30pm. E.X.L. de Andrade  (Universidade Estadual Paulista, Brasil).
Title: "Asymptotic for Laguerre-Sobolev orthogonal polynomials for non-coheret pairs of type I."
Abstract: This paper deals with asymptotic relations associated with the
orthogonal polynomials with respect to a class of Laguerre-Sobolev
inner products.  The inner products are such that the associated
pairs of  measures are not within the concept of  coherent pairs of
measures.
Viernes, 30 de mayo de 2008.
Lugar: Seminario de Matemática Aplicada, Universidad de Almería. 
Sesión: 11.00am. Dra. Eva Touris  (Universidad Carlos III de Madrid).
Título: "Una nueva caracterización para la Hiperbolicidad de Gromov con curvatura variable."
Resúmen: En este trabajo probamos que, de cara a comprobar la hiperbolicidad
de superficies con curvatura variable negativa, K < -k^2<0, sólo necesitamos
comprobar la condición de Rips (que es equivalente a la hiperbolicidad de
Gromov) para una clase pequeña de triángulos, normalmente, aquello que están
contenidos en geodésicas simples y cerradas. Este resultado es, de hecho,
una nueva caracterización para la hiperbolicidad de Gromov de este tipo de
superficies.
Sesión: 12.00am. Dr. Jorge Arvesú  (Universidad Carlos III de Madrid).
Título: "Unpublished notes on the irrationality of $\zeta(n)$ for odd arguments and associated Riemann-Hilbert problem."
Resúmen: Some previous results concerning the irrationality of $\zeta(3)$ are shown.
A new approach for the general problem form the rational approximation point
of view based on Riemann-Hilbert tools will be given. Finally, a detailed
discussion for solving the irrationality of $\zeta(3)$ and $\zeta(5)$ will
be presented. This talk is partially based on a join contribution with P.
Deift and J. Geronimo.
Sesión: 13.00am. Dr. A. Sri Ranga  (Sao Jose do Rio Prieto, Brasil).
Título: "Asymptotics for Gegenbauer-Sobolev and Hermite-Sobolev orthogonal polynomials associated with non-coherent pairs of measures."
Resumen:  aquí.  
Martes, 27 de mayo de 2008.
Lugar: Seminario de Matemática Aplicada, Universidad de Almería. 
Sesión: 10.00am. Dr. Ruyman Cruz Barroso  (Universidad de La Laguna).
Título: "Problemas de autovalores equivalentes para fórmulas de cuadratura de Szegö."
Resumen:  aquí.  
 Jueves 10 de abril de 2008. Lugar: Sala de Claustro, Facultad de Ciencias, Universidad de Granada. 
Sesión: 10.00h. Dra. Chelo Ferreira  (Universidad de Zaragoza) y Dra. Ester Pérez Sinusía (Universidad Pública de Navarra).
Titulo: "Aproximación asintótica de integrales. Aplicaciones en el estudio de problemas de perturbación singular."
Resumen:  aquí.  

Jueves 27 de marzo de 2008. Lugar: Aulario IV, Universidad de Almería. 
Sesión: 10.00h. Dr. Maxim Yattselev (INRIA, Sophia-Antipolis, Francia).
Titulo: "Hon-Hermitian Orthogonal Polynomials with Varying Weights on an Arc"
Resumen: We consider multipoint Padé approximation of Cauchy transforms of complex measures. We show that if the support of a measure is a piecewise analytic Jordan arc and the density of this measure is sufficiently smooth, then the diagonal multipoint Padé approximants associated with "admissible" interpolation schemes converge locally uniformly to the approximated Cauchy transform. The existence of "admissible" interpolation schemes is discussed for the case where support is an analytic Jordan arc. As usual, the asymptotic behavior of Padé approximants is deduced from the analysis of underlying non-Hermitian orthogonal polynomials. 

Jueves 31 de enero. Lugar: Sala de audiovisuales, Facultad de Ciencias, Universidad de Granada. 
Sesión: 12.00h. Dr. Ramón Orive (Universidad de La Laguna, Tenerife).
Titulo: "Estudio asintótico de polinomios ortogonales de Sobolev con pesos exponenciales"
Resumen: aquí. 

Jueves 13 de diciembre. Lugar: Sala de audiovisuales, Facultad de Ciencias, Universidad de Granada. 
Sesión: 11.00h. Dr. Miguel A. Piñar (Universidad de Granada).
Titulo: "Polynomials and Partial Differential Equations on the Unit Ball"
Resumen: Orthogonal polynomials of degree n with respect to the weight function $W_\mu(x) = (1-\|x\|^2)^\mu$ on the unit ball in Rd are known to satisfy the partial differential equation $$ [ \Delta - \la x, \nabla \ra^2 - (2 \mu +d) \la x, \nabla \ra   ] P = -n(n+2 \mu+d) P $$ for $\mu > -1$. The singular case of \mu = -1,-2, ... is studied in this work. Explicit polynomial solutions are constructed and the equation for \nu = -2,-3,... is shown to have complete polynomial solutions if the dimension d is odd. The orthogonality of the solution is also discussed. [*.pdf]

Sesión: 12.00h. Dr. Andrei Martínez-Finkelshtein (Universidad de Almería).
Titulo: "Non-intersecting squared Bessel paths and multiple orthogonal polynomials for modified Bessel weights"
Resumen: We study a model of $n$ non-intersecting squared Bessel processes in the confluent case: all paths start at time $t = 0$ at the same positive value $x = a$, remain positive, and are conditioned to end at time $t = T$ at $x = 0$. In the limit $n \to \infty$, after appropriate rescaling, the paths fill out a region in the $tx$-plane that we describe explicitly. In particular, the paths initially stay away from the hard edge at $x = 0$, but at a certain critical time $t^*$ the smallest paths hit the hard edge and from then on are stuck to it. For $t \neq t^*$ we obtain the usual scaling limits from random matrix theory, namely the sine, Airy, and Bessel kernels. A key fact is that the positions of the paths at any time $t$ constitute a multiple orthogonal polynomial ensemble, corresponding to a system of two modified Bessel-type weights. As a consequence, there is a $3 \times 3$ matrix valued Riemann-Hilbert problem characterizing this model, that we analyze in the large $n$ limit using the Deift-Zhou steepest descent method. There are some novel ingredients in the Riemann-Hilbert analysis that are of independent interest. 

Lunes 5 de noviembre. Lugar: Universidad de Almería. CITE III Seminario de Matemática Aplicada
Sesión: 10.00h. Dr. Leonid Golinskiy, de Institute Low Temperatures, Kharkiv, Ucrania.
Titulo: "Inverse spectral problems for finite CMV matrices"
Resumen: For finite CMV matrices the classical inverse spectral problems (ISP) are studied. We solve the ISP of reconstructing a CMV matrix by its spectral measure, by two spectra of CMV matrices with different "boundary condition", by its spectrum and the spectrum of its unitary truncation. The ISP for Alexandrov's matrices and mixed ISP are discussed. 
Sesión: 11.00h. Dr. Andras Kroo, de Institute Renyi of Mathematics, Hungría.
Titulo: "Classical Polynomial Inequalities in Several Variables"
Resumen: Classical polynomial inequalities of Markov, Bernstein, Chebyshev, Remez play a central role in Approximation Theory. In past 20 years a considerable effort was made in order to extend these inequalities to multivariate polynomials. The case of several variables is much "richer" in the sense that here the results are closely related to the geometry of underlying domains. In this talk we shall give a survey of these results . 

Jueves 18 de octubre. Lugar: Universidad de Almería. CITE III Seminario de Matemática Aplicada
Sesión: 11.00h. Dr. Jeffrey Geronimo, de Georgia Institute of Technology.
Titulo: "Two variable Szego-Bernstein measures"

Resumen: Bernstein -Szego measures have played an important role in the theory of orthogonal polynomials. 
Scattering theory, the Szego function and the Jost function were developments stemming from these
measures. We will discuss a class of two variable Bernstein-Szego measures.
Jueves 13 de septiembre. Lugar: Universidad de Almería. CITE III Seminario de Matemática Aplicada
Sesión 11.00h. Dr. Alexander Aptekarev "Higher-Order Three-Term Recurrences and Asymptotics of Multiple Orthogonal Polynomials"
Sesión 12.30h. Dr. Helbert Stahl "Rational bet appriximation (-\infty,0]" [*.pdf]

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Ultima actualización de esta página, 19 de septiembre de 2008.