Elliptic Problems and Applications in Geometry

Location

BEIRUT
,
Lebanon

Dates

to

Presentation

Interactions between analysis and geometry are of considerable importance in mathematics. The famous Yamabe problem and Perelman’s proof of Poincaré are remarkable illustrations of these interactions. The aim of this school is to provide an introduction to some of these topics, focusing on geometric problems that are expressed in terms of elliptic equations.

The first part of the school deals with two classical subjects : prescription of curvature and spectral geometry. These topics have a fairly long history, but are still subject of active research. We will provide participants with basic knowledge on these subjects before presenting some recent results and open problems. Thus, the school will begin with a general introduction to elliptic problems in Euclidean space and manifolds as well as the variatonal method to solve elliptic PDE. Regarding spectral geometry, we will concentrate on bounded domains of the Euclidean space and Riemannian surfaces, so that only a basic understanding of Riemannian geometry is necessary. As for the prescribed curvature problem, it will be discussed in the case of compact surfaces so as to minimize the needed geometric prerequisites.

The second part of the school is devoted to more specialized topics, such as quantitative isoperimetric and singular spectral pertubations.

There will be also of interactive sessions devoted to examples, exercises and numerical experiments.

Administrative and scientific coordinators

Ali Wehbe (Université Libanaise,
Lebanon
, )
Bruno Colbois (Université de Neuchâtel,
Switzerland
, )

Scientific program

Course 1: "Singular Spectral Perturbations", Colette Anné (University of Nantes, France)

Course 2: "Numerical methods for the computation of eigenmodes", Virginie Bonnaillie-Noël (ENS Paris, France)

Course 3: "Introduction to spectral geometry", Bruno Colbois (University of Neuchatel, Switzerland)

Course 4: "Prescribed Gaussian curvature", Ali Fardoun (University of Brest, France)

Course 5: "Spectral geometry of the Steklov problem", Alexandre Girouard (University of Laval, Canada)

Course 6: "A tour on Riesz means and eigenvalue bounds on euclideans domains", Asma Hassannezhed (University of Bristol, United Kingdom)

Course 7: "Variational methods for elliptic problems", Ali Wehbe (Lebanese University, Lebanon)

Website of the school

How to participate

For registration and application to a CIMPA financial support, follow the instructions given here

Deadline for registration and application:  November 15, 2017.