Conferencias invitadas

A new class of FBI transforms and applications

In this talk we will introduce a new class of FBI transforms using weight functions  (which includes the subclass of Sj\"ostrand's FBI transforms used by M. Christ) that is well suited when dealing with ultradifferentiable functions and ultradistributions  defined by  weight functions in the sense of Braun, Meise and Taylor (BMT). We show how to characterize  local regularity of BMT  ultradistributions using this wider class of FBI  transform and,  as an application, we characterize the BMT vectors in terms of this class of FBI transforms and prove a relation between BMT local regularity and BMT vectors.

Espectro del Laplaciano en esferas no redondas

Describiremos el espectro del operador de Laplace-Beltrami asociado a métricas Riemannianas en esferas de dimensión impar que son ``homogéneas'', en el sentido que su grupo de isometrías actúa transitivamente. La intención es que la charla sea entendible para una audiencia no familiarizada con geometría Riemanniana.

Convergencia monomial y el problema de Lempert

Resumen

Fourier decay of self-similar measures on the complex plane

We prove that the Fourier transform of self-similar measures on the complex plane has fast decay outside of a very sparse set of frequencies, with quantitative estimates, extending the results obtained in the real line by R. Kaufman. Also we derive several applications concerning correlation dimension and Frostman exponent of complex Bernoulli convolutions. Furthermore, we present a generalization for a particular case on Rd, with d ≥ 3. The results are based on a joint work with Andrea Olivo.

Ondículas y aplicaciones en espacios métricos

La transformada de Fourier resulta clave en varios problemas del análisis armónico real. Al salirse del caso euclidiano sin embargo, no es claro si esta herramienta está disponible o cómo se puede reproducir. Una manera de sortear este inconveniente en ciertos espacios métricos es desarrollando una generalización del análisis Littlewood-Paley y las fórmulas de reproducción de Calderón, y a partir de allí construir un sistema de ondículas. En esta charla veremos como estos sistemas permiten, al igual que en R^n, obtener resultados de regularidad local y global para distintos espacios de funciones.

Some recent advances about uncertainty principles

We will review some recent results about uncertainty principles and discuss two applications: one in the asymptotic behavior of solutions to the harmonic oscillator, and another one related to embbeding problem of some homogeneous Paley-Wiener spaces.

Optimal control for a SIR model with limited hospitalized patients

We study necessary conditions for an optimal control problem for a SIR model with a running state constraint that models the limitation on the amount of patients supported by the intensive care.

Medidas de soporte prefijado y dimensión de regularidad (Assouad) arbitraria

Resumen