Hypatia Graduate Summer School 2022

This summer school series aims at training their participants in key strategic problems in mathematics and their applications, with the core idea that theory and applications strengthen each other. The school is focused in training of young researchers whilst opening new fields for senior ones.

The Hypatia Graduate Summer School will consist in two keynote courses on subjects of exceptional promise and scientific importance delivered by highly distinguished speakers in the area plus a high-level colloquium on a complementary subject.

The Hypatia Graduate Summer School will be developed in an informal atmosphere based on discussions, exchange of ideas and critical analysis of results. Moreover, to honour its namesake, it is committed to work under a friendly gender perspective that highlights the role of women in mathematics and encourages and helps the participation and promotion of young female researchers at a professional level.

Lecturer: M. Ángeles García-Ferrero (BCAM)

Abstract:

The Calderón problem is a prototypical inverse problem on which medical and geological imaging techniques are based. Roughly speaking, the aim is the determination the conductivity of a medium by measurements of voltages and currents on its boundary. The problem can be mathematically formulated as the determination of an unknown potential in a Schrödinger equation from the knowledge of the so-called Dirichlet-to-Neumann map.

In this course, we will address the questions of uniqueness and stability for the classical Calderón problem. We will also introduce the Calderón problem associated to other operators.

Lecturer: Javier Gómez-Serrano (UB-Brown-CRM)

Abstract:

There are many settings in fluid mechanics modeled by a free boundary. These contour dynamics problems are given by basic fluid mechanics systems, such as the Euler equation, Darcy´s law and the Quasi-geostrophic equation and many interesting problems arise. For example the water wave problem, the Muskat problem, the one and two-phase Hele-Shaw problem or the evolution of sharp fronts. However, many of these are not or partially understood and in particular the global existence vs finite time singularity formation question presents a big challenge. In this lectures I will address some of the recent advances that have happened lately.

Lecturer: Xavier Ros-Oton (ICREA-UB-CRM)

Abstract:

Free boundary problems (FBP) are those described by PDE that exhibit a priori unknown (free) interfaces or boundaries. Such type of problems appear in Physics, Geometry, Probability, Biology or Finance, and the study of solutions and free boundaries uses methods from PDE, Calculus of Variations, and Geometric Measure Theory.

The Stefan problem, which describes the melting of ice, is one of the most classical and motivating FBP. The aim of this course is to give an overview of the main known regularity results for free boundaries in this setting, and present some recent results concerning the set of singular points.

If you wish to attend the HYPATIA Colloquium please confirm your attendance by filling out the following form:

REGISTRATION FEE IN-PERSON ATTENDANCE: 200€

REGISTRATION FEE ONLINE ATTENDANCE: 25€

REGISTRATION DEADLINE: 10/06/2022

*Registration includes: coffee breaks and reception.

IF YOUR INSTITUTION COVERS YOUR REGISTRATION FEE: Please note that, in case your institution is paying for the registration via bank transfer, you will have to indicate your institution details and choose “Transfer” as the payment method at the end of the process.

HYPATIA es una actividad relacionada con la RED de ecuaciones en derivadas parciales no locales y aplicaciones, RED2018-102650-T.