Speaker: Dr. Sergio Medina, MDC.
Title: On the convergence of Hermite-Padé approximants.
Abstract: Since 1873, when Charles Hermite publishes his proof of the transcendence of e making use of theHermite-Padé approximants of one system of exponentials the theory of simultaneous rational approximations have been an invaluable tool in many mathematical fields. In addition to number theory, these approximants are connected with the theory of orthogonal polynomials, Riemann-Hilbert problems, models coming from random matrix theory, biorthogonal emsembles , and partial differential equations among others. In this talk we will present some recent results about the uniform convergence of these Hermite-Padé approximants and one application related with the solutions of the Degasperis-Procesi differential equations.