Cours I - Thomas Alazard (Centre Borelli, Ecole Normale Supérieure Paris-Saclay)

Control and Stabilization of the water-waves equations.

These lectures focus on the controllability and stabilization of gravity-capillary water waves. In particular, I will present the multiplier method and show how it can be applied to study damping by an absorbing beach where the energy of the water wave is dissipated using variations in the external pressure. 

Cours II - Freddy Bouchet (Groupe climat et physique statistique, Ecole Normale Supérieure de Lyon)

Theoretical physics and mathematical problems for climate, atmosphere and ocean dynamics

A first part of these lectures will be devoted to a review of a set fundamental problems in climate, atmosphere and ocean dynamics and their connections to different fields of theoretical physics and mathematics: partial differential equations, probability, stochastic processes, statistics, machine learning, statistical physics, turbulence theory and topological effects in geophysical fluid dynamics.  The aim will be to give an overview, necessarily limited and biased, of where and why mathematicians and physicists have an important role to play in these fields in the future.
A second part will present a few of my recent works related to climate and atmosphere dynamics. We will consider recent developments in theoretical physics for the study of rare events, and their applications for the study of extreme heat waves and abrupt climate change. We will also discuss the role of large deviation theory, in connection with kinetic theory, in order to improve our understanding of turbulent flows.

Cours III - Clémentine Prieur (AIRSEA, Laboratoire Jean Kuntzmann, Université Grenoble Alpes)

Analyse de sensibilité globale pour modèles complexes

Many mathematical models use a large number of poorly-known parameters as inputs. Sensitivity analysis aims at quantifying the influence of each of these parameters (or of each subset of these parameters) on specific quantities of interest. More generally it helps in understanding model behavior, characterizing uncertainty, improving model calibration, etc. In these lectures I will focus on Global Sensitivity Analysis which is based on the modeling of input uncertain parameters by a probability distribution. There exist various measures built in that paradigm. I will mainly present variance based measures, in the framework of scalar, vectorial and functional outputs, in the framework of independent or dependent inputs. I will also discuss different alternatives for the estimation of these measures. Most of the estimation procedures rely on an input/output sample. The lectures will be illustrated on Notebooks.