Algebra and Geometry track

Contact person: Dimitri Wyss

Below we explain the structure of the Algebra and Geometry track. Not all courses are given each year. If you decide to focus on the Algebra and Geometry track, we suggest that you take MOST of the courses below during the third year of your bachelors and during your masters. You have the freedom how to interpret "most", but we suggest you interpret it based on your mathematical taste. That is, you take all courses that are in topics that you like the most. It is very important that you create a coherent set of courses for yourself. That is, you learn certain aspects of pure math deeply, in a way that the courses strengthen each other. In particular, you should be careful to take all prerequisite courses to the courses that you will want to take later on. You can have a rough idea of the dependencies of the courses by looking at the table below. The columns of this table are arranged based on "prerequisite channels" (the general courses, up to BA 5, are for all channels). We also remark that a big part of pure math is analysis, so for almost all of you it might be a good idea to complement the offering below with some courses from the analysis track.

The main areas present in the Algebra and Geometry track (in alphabetical order) are:

Many of the courses of the track are interdisciplinary, so it is hard to assign them to only one of the above areas. So, the way couses are assigned in the following table to columns is only a guideline. Also, some of the courses listed in the table are not given every year. Such courses are typically not essential prerequisites for other courses. Discounting these discrepancies, the table below can be used well to understand a first approximation of the "prerequisite channels" of the track. 











BA 1


Structures algébriques

Linear Algebra I

BA 2


Linear algebra II

BA 3


Théorie des groupes

Espaces métriques et topologiques

Géométrie différentielle

BA 4


Anneaux et corps


BA 5


Algebra IV - Rings and modules

Algebra V - Galois theory



Differential geometry II

Smooth manifolds


Number theory I.a

Algebraic number theory


Number theory I.b

Analytic number theory

Number theory 1.c

Combinatorial number theory


Algebraic geometry I



Geometry III

Riemannian geometry

Representation theory


Topology III


Topological groups

MA1 (joint)

Student seminar in pure mathematics

Riemann surfaces



geometry II

Schemes and sheaves

Differential Geometry IV

Introduction to general relativity

Lie groups and algebras

Ergodic theory

Topology IV.a

Algebraic K-theory




Algebraic geometry III

Selected topics

  Abstract analysis on groups

Number theory II.a

Modular forms

Topology IV.b

Homotopy theory

Quantum (loop) groups and quivers

Number theory II.b



For more information please click below on the name of the research group that you are most interested in (names of the groups in alphabetical order):

Name of the group & link Name of the professor
Algebraic Geometry Prof. Zsolt Patakfalvi
Analytic Number Theory Prof. Philippe Michel
Arithmetic Geometry Prof. Dimitri Stelio Wyss
Differential Geometry Prof. Marc Troyanov
Ergodic Theory Prof. Florian Richter
Ergodic and Geometric Group Theory Prof. Nicolas Monod
Number Theory Prof. Maryna Viazovska
Reductive Groups Prof. Donna Testermann
Topology Prof. Kahtryn Hess Bellwald
General Relativity Prof. Georgios Moschidis

General description :

A big part of today's theoretical mathematical research has some algebraic or geometric flavor to it. Examples are endless: number theory, representation theory, differential geometry, algebraic geometry, arithmetic geometry, homotopy theory, geometric group theory, low dimensional topology, symplectic geometry, algebraic combinatorics, combinatorial geometry, and others, including many different combinations of the above listed fields. This track gathers some of the topics that are important to study for most of these fields. However, it is important to stress that for many of the above areas it is similarly essential to take some of the analysis courses. For that please consult the links above where the research groups at EPFL list the courses suggested to take to be able to conduct research in the given group. 

Related Minors :