The first part is devoted to Monge and Kantorovitch problems, discussing the existence and the properties of the optimal plan. The second part introduces the Wasserstein distance on measures and develops applications of optimal transport to PDEs, functiona ...
This course serves as an introduction to classical differential geometry, which studies the geometric properties of curves and surfaces in the Euclidean space. ...
The goal of the course is to introduce relativistic quantum field theory as the conceptual and mathematical framework describing fundamental interactions. ...
This course provides an overview of key advances in continuous optimization and statistical analysis for machine learning. We review recent learning formulations and models as well as their guarantees
A first graduate course in algorithms, this course assumes minimal background, but moves rapidly. The objective is to learn the main techniques of algorithm analysis and design, while building a repertory of basic algorithmic solutions to problems in many ...
L'objectif du cours est d'introduire les notions de base de l'algèbre linéaire (pour les futurs mathématiciens) et de démontrer rigoureusement les résultats principaux de ce sujet. ...
This is an introductory course on Elliptic Partial Differential Equations. The course will cover the theory of both classical and generalized (weak) solutions of elliptic PDEs. ...
The student will learn state-of-the-art algorithms for solving differential equations. The analysis and implementation of these algorithms will be discussed in some detail. ...