Studying Geometry at EPFL

Despite the fact that geometry is, together with arithmetic, the oldest branch of mathematics, the subject is still extremely alive and a major part of both mathematical culture and contemporary research developments.

Nowadays, Geometry is no longer a single subject, but it has split in a variety of different subjects; each with its own problems, techniques and results. Very roughly one can divide the area in: Algebraic Geometry, Differential Geometry, Metric Geometry and Discrete and Computational Geometry etc. We could also add various fields such as Geometric Group Theory or Dynamical Systems.

A student interested in geometry should therefore partially adapt his choice of courses to the type of geometry he is interested in.

For algebraic geometry, see the page

For differential geometry, we recommend :

Bachelor (second year) :

    •    Espaces métriques et topologiques
    •    Théorie des groupes
    •    Topologie
 Bachelor (third year):

    •    Introduction aux variétés différentiables
    •    Équations différentielles ordinaires
    •    Chapitres choisis de géométrie : surfaces minimales
    •    Mesure et intégration
    •    Analyse fonctionnelle I
    •    Algèbre de Lie (pas donné 2017/2018)
    •    Espaces de Sobolev et équations elliptiques
    •    Homology and cohomology
    •    Introduction aux équations aux dérivées partielles

Master :

    •    Introduction à la géométrie riemannienne
    •    Riemann surfaces
    •    Lie Groups
    •    Differential geometry of framed curves
    •    Analyse fonctionnelle II
    •    Elliptic PDEs
    •    Parabolic and hyperbolic PDEs

The following is a useful list of courses for people interested in metric and/or discrete geometry:

Please note that not every course is given each year. Also dont be too much influenced by this list, each student should choose his/her curricula coherently but according to one’s taste and preferences. 
Enjoy your study and enjoy geometry.

Marc Troyanov
May 2017