The goal of this course is to give an introduction to the theory of distributions and cover the fundamental results of Sobolev spaces including fractional spaces that appear in the interpolation theory. Those notions are central to the study of partial dif ...
The theme of the working group varies from year to year. Examples of recent topics studied include: Galois theory of ring spectra, duality in algebra and topology, and topological algebraic geometry. ...
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 ...
P-adic numbers are a number theoretic analogue of the real numbers, which interpolate between arithmetics, analysis and geometry. In this course we study their basic properties and give various applications, notably we will prove rationality of the Weil Ze ...
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 ...
We introduce locally convex vector spaces. As an example we treat the space of test functions and the space of distributions. In the second part of the course, we discuss differential calculus in Banach spaces and some elements from nonlinear functional an ...
This doctoral course provides an introduction to optimal control covering fundamental theory, numerical implementation and problem formulation for applications. ...
Non-positive curvature is a fundamental aspect of geometry appearing in Euclidean spaces, hyperbolic spaces, trees, buildings and many more spaces. We study it with the general but powerful tool of CA ...
Ce cours ambitionne de présenter les mathématiques de la mécanique quantique, et plus généralement de la physique quantique. Il s'adresse essentiellement aux physiciens, ou a des mathématiciens intéressés dans le domaine. ...