## 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