Summer school EUR MINT 2025 -- Control, Inverse Problems and Spectral Theory

Abstracts

2. A few techniques to achieve invisibility in waveguides

Lucas Chesnel (Inria)

The aim of this lecture is to consider a concrete problem, namely the identification of situations of invisibility in waveguides, to present techniques and tools that may be useful in various fields of applied mathematics. To be more specific, we will be interested in the propagation of acoustic waves in guides which are unbounded in one direction. In general, the diffraction of an incident...

4. Inverse problems in the wave equation: from stability to parameter reconstruction

Lucie Baudouin (LAAS-CNRS)

In this lecture, we will present approaches based on Carleman estimates of several questions related to inverse problems for evolution partial differential equations. The focus will be the recovery of parameters in the wave equation posed in a bounded domain with Dirichlet boundary conditions.
Carleman estimates are a type of weighted energy inequalities. They are particularly useful in...

1. Spectral geometry: old questions and new answers

David Krejcirik

Spectral geometry is concerned with the interaction between the spectrum of linear differential operators and the geometry of underlying Riemannian manifolds. The goal of the lecture is to acquaint the student with classical problems as well as the most recent developments in the field. The emphasis is put on the Laplace operator in Euclidean domains, subject to Dirichlet, Neumann and Robin...

3. Time Iteration Methods for Controllability

Frédéric Marbach (DMA, ENS Ulm, CNRS)

This course explores several important strategies ubiquitous in control theory, presenting them as time iteration methods, where each time step progressively brings us closer to achieving the control objective. This course aims to provide an accessible introduction to these techniques.

For ordinary differential equations (ODEs), we will focus on the tangent vector method, which allows us to...