Covering small sets by graphs of functions

Jueves 1 de junio, 12h

Seminario del Departamento
El Departamento de Matemáticas y Estadística de la Universidad Torcuato Di Tella invita a la charla sobre Covering small sets by graphs of functions a cargo de Eino Rossi, becario postdoctoral en UTDT. Recibió su doctorado de la Universidad de Jyväskylä, Finlandia.

Abstract
In a recent collaboration with Pablo Shmerkin, we studied when a set can be covered by a graph of a function. Consider for example a set in the plane. If the orthogonal projection of the set to the x-axis is injective, then the inverse of the set is well defined and can be extended to a function from x-axis to reals. Thus we have obtained the desired covering. More specifically, we study the regularity of the inverse of the projection. We obtain that when the box dimension of the set is small, then for almost every rotation of the set there exists a cover by a Hölder continuous function. Here, small box dimension means that the set can be covered by small boxes of equal side length and the amount of the boxes needed is comparable to a small power of the inverse of side length of the boxes. Moreover we obtain estimates for the dimension of the set of the exceptional rotations, where a cover by a Hölder graph was not possible. For a specific class of sets, called homogenous sets, we find coverings by Lipschitz graphs, which is much much better, in the sense of regularity, than having a covering by a Hölder graph.

La charla será en inglés (sin traducción).

Lugar: Sala de Conferencias (edificio Sáenz Valiente) Campus Alcorta: Av. Figueroa Alcorta 7350, Ciudad de Buenos Aires.
Contacto: Asistente Matemática