The 'probabilistic method' is a fundamental tool in combinatorics. The basic idea is as follows: to prove that an object (for example, graph) with certain properties exists, it suffices to prove that if the object is chosen at random, then it has the desir ...
We develop, analyze and implement numerical algorithms to solve optimization problems of the form min f(x) where x is a point on a smooth manifold. To this end, we first study differential and Riemannian geometry (with a focus dictated by computational con ...
Le cours vise a familiariser les etudiants avec l'histoire de l'environnement et des paysages, et avec la maniere dont les preoccupations environnementales amenent a repenser aujourd'hui le sens et les principes de l'architecture et des disciplines de pr ...
This course will provide an introduction to model category theory, which is an abstract framework for generalizing homotopy theory beyond topological spaces and continuous maps. We will study numerous examples of model categories and their applications in ...
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 ...
This course is intended for students who want to understand modern large-scale data analysis systems and database systems. It covers a wide range of topics and technologies, and will prepare students to be able to build such systems as well as read and und ...
This course covers the following topics: Introduction to conic optimization, Duality in conic programming, Sums of squares/ SemideFinite relaxation for independence number and chromatic number, Harmonic analysis on [owe, sets, Lasserre's hierarchy, Packing ...