José Luis Rubio de Francia (1949-1988) nació en Miedes, Zaragoza. Se licenció y doctoró en Matemáticas por la Universidad de Zaragoza. Su tesis doctoral, "Integración en grupos clásicos y abstractos con aplicaciones al Análisis de Fourier", fue dirigida por el profesor Luis Vigil. Desde 1989 el Departamento de Matemáticas viene celebrando anualmente un coloquio especial para honrar la memoria de José Luis (véase la lista de conferenciantes más abajo).
Por su parte la Real Sociedad Matemática Española, con el patrocinio de la Universidad Autónoma de Madrid y la Universidad de Zaragoza, convoca anualmente el premio "José Luis Rubio de Francia" para jóvenes investigadores e investigadoras en Matemáticas.
ONLINE: https://us06web.zoom.us/j/82650507551
In this talk we will discuss a few sharp inequalities related to the Fourier transform, within two themes: Fourier restriction theory and Fourier uncertainty principles. In the first theme, we will be mainly concerned with the classical restriction setup for quadratic surfaces (spheres, paraboloids, cones and hyperboloids) arising from the seminal work of Strichartz of 1977. Related questions involving mixed norms and stability issues will also be addressed. In the second theme, we will address the problem of prescribing the sign of a function and its Fourier transform at infinity, and doing this in an optimal way (in an appropriate sense). This phenomenon was introduced by Bourgain, Kahane and Clozel in 2010 under the name of "sign Fourier uncertainty", and brings interesting connections to the sphere packing problem.
In this talk I will present several examples of measures that arise naturally in different contexts, for example PDEs and free boundary regularity problems. I will discuss how the infinitesimal properties of a measure yield a great deal of information about the measure and its support. In turn this sheds light on the original problem which gave rise to the measure in question