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 ...
Discrete mathematics is a discipline with applications to almost all areas of study. It provides a set of indispensable tools to computer science in particular. This course reviews (familiar) topics as diverse as mathematical reasoning, combinatorics, disc ...
The students gain an in-depth knowledge of several current and emerging areas of theoretical computer science. The course familiarizes them with advanced techniques, and develops an understanding of fundamental questions that underlie some of the key probl ...
Algebraic geometry is the common language for many branches of modern research in mathematics. This course gives an introduction to this field by studying algebraic curves and their intersection theory. ...
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 ...
Ce cours donne une introduction rigoureuse au principaux thèmes de la théorie des équations différentielles ordinaires (EDO). Les EDO sont fondamentales pour l'étude des systèmes dynamiques et des équations aux dérivées partielles. Des applications dans ce ...