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 ...
On étudie des notions de topologie générale: unions et quotients d'espaces topologiques; on approfondit les notions de revêtements et de groupe fondamental,et d'attachements de cellules et on démontre le Théorème de Seifert-van Kampen. Des exemples de surf ...
Singular cohomology is defined by dualizing the singular chain complex for spaces. We will study its basic properties, see how it acquires a multiplicative structure and becomes a graded commutative algebra. We study an algebraic version, namely group coho ...
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 is the first part of a two-semester course covering various legal topics related to technology and sustainability issues. After an introduction to the legal system, students will study contract reading and data protection. Some tax aspects will be cov ...
The goal of this course/seminar is to introduce the students to some contemporary aspects of geometric group theory. Emphasis will be put on Artin's Braid groups and Thompson's groups. ...
This summer school will explore basic concepts as well as recent developments in optimization, interpolation, and modular forms. There will be short courses as well as several standalone lectures by invited researchers. The school is aimed toward masterâ ...