Machine learning and data analysis are becoming increasingly central in sciences including physics. In this course, fundamental principles and methods of machine learning will be introduced and practised. ...
The students understand tools from the statistical physics of disordered systems, and apply them to study computational and statistical problems in graph theory, discrete optimisation, inference and machine learning. ...
This course presents numerical methods to solve mathematical problems such as systems of linear and nonlinear equations, function approximation, integration and differentiation, and differential equations. ...
This course is an introduction to the theory of Riemann surfaces. Riemann surfaces naturally appear is mathematics in many different ways: as a result of analytic continuation, as quotients of complex domains under discontinuous group actions, as algebraic ...
Concepts de base de l'analyse fonctionnelle linéaire: opérateurs bornés, opérateurs compacts, théorie spectrale pour les opérateurs symétriques et compacts, le théorème de Hahn-Banach, les théorèmes de l'application ouverte et du graphe fermé. ...
Linear and nonlinear dynamical systems are found in all fields of science and engineering. After a short review of linear system theory, the class will explain and develop the main tools for the qualitative analysis of nonlinear systems, both in discrete-t ...
We will present the theory of PDEs and of transport equations with rough (non Lipschitz) velocity fields, address both the renormalisation theory by DiPerna-Lions-Ambrosio and its quantitative Lagrangian counterpart and show applications to mixing estimate ...