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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:
 algebraic geometry
 differential geometry
 group theory & representation theory (written only as group theory in the table below)
 number theory
 topology
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.
algebraic geometry 
differential geometry 
group theory 
number theory 
topology  
BA 1 (joint) 
Structures algébriques 

Linear Algebra I 

BA 2 (joint) 
Linear algebra II  
BA 3 (joint) 
Théorie des groupes 

Espaces métriques et topologiques 

Géométrie différentielle 

BA 4 (joint) 
Anneaux et corps 

Topologie 

BA 5 (joint) 
Algebra IV  Rings and modules 

Algebra V  Galois theory 

BA5 

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 

BA6 
Algebraic geometry I Curves 
Differential Geometry III Riemannian geometry 
Representation theory 
Topology III Homology 

Topological groups 

MA1 (joint) 
Student seminar in pure mathematics 

Riemann surfaces 

MA1 
Algebraic geometry II Schemes and sheaves 
Differential Geometry IV Introduction to general relativity 
Lie groups and algebras 
Ergodic theory 
Topology IV.a Algebraic Ktheory 




MA2 
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 Cryptography 


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 :
 Analysis track
 Algorithmic and Dirscrete Mathematics track
 Probability track