Homology is one of the most important tools to study topological spaces and it plays an important role in many fields of mathematics. The aim of this course is to introduce this notion, understand its properties and learn how to compute it. There will be m ...
The numerical simulation of quantum systems plays a central role in modern physics. This course gives an introduction to key simulation approaches, through lectures and practical programming exercises. Simulation methods based both on classical and quantum ...
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 ...
We propose an introduction to homotopy theory for topological spaces. We define higher homotopy groups and relate them to homology groups. We introduce (co)fibration sequences, loop spaces, and suspensions. We study long exact sequences. We construct Eilen ...
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 ...
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 introduces the foundations of information retrieval, data mining and knowledge bases, which constitute the foundations of today's Web-based distributed information systems. ...
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 ...