Seminario de Análisis y Geometría

2016-09-13
16:00hrs.

Rémy Rodiac. Pontificia Universidad Católica de Chile
Regularity of limiting vorticities of the Ginzburg-Landau equations
Sala 2, Facultad de Matemáticas UC
Abstract:
Limiting vorticities in the Ginzburg-Landau theory are Radon measures that describe the location of the vortices of the model when the parameter $\epsilon$ is small. Sandier-Serfaty gave some critical conditions that are satisfied by such limiting vorticities. One can then ask about the regularity of these objects. In the case withouth magnetic field the problem is equivalent to the study of stationary harmonic functions whose Laplacian are Radon measures. We will prove that such functions can be written locally as the absolute value of an harmonic function. Thus its Laplacian is concentrated (locally) on the zero set of an harmonic function (a union of smooth curves). We will also give some results in the case with magnetic field.

2016-08-30
16:00hrs.

Mariel Sáez. Pontificia Universidad Católica de Chile
Fractional Mena Curvature Flow
Sala 2 Facultad de Matemáticas UC
Abstract:
In this talk I will discuss a fractional analog to the classical mean curvature flow. Namely, we consider the evolution of surfaces with normal speed equal to the fractional mean curvature and analyze their behavior under suitable assumptions. I will discuss in more depth the evolution of graphical hyper-surfaces, which is an important model in the local case.

This is joint work with Enrico Valdinoci