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 https://wiki.epfl.ch/sma-teachers/algebra-geometry
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:
- Graph theory (Bachelor)
- Convexity
- Combinatorial optimization
- Combinatorial Geometry
- Packing and covering
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