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Algebra and Geometry track
(last modified 19.04.2022)
Contact person: Professor Zsolt Patakfalvi
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, some courses are so interdisciplinary that they are put in many columns (for example, "Riemann surfaces"). 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 

Introduction au courbes et surfaces 

BA 4 (joint) 
Anneaux et corps; Topologie 

BA 5 (joint) 
Rings and modules 

Galois theory 

Lie algebras 

BA5 
Rings and modules 
Introduction to differentiable manifolds 
Coxeter groups 
Introuction to analytic number theory 

Spaces of nonpositive curvature and groups 

BA6 
Algebraic curves 
Introduction to Differential Geometry 
Representation theory 
Algebraic number theory 
Algebraic topology 
Representation theory of finite groups 
Combinatorial number theory 

MA1 
Modern algebraic geometry 
Riemann surfaces 
Analysis on groups 
Automorphic forms and Lfunctions 
Homotopy theory 
Riemann surfaces 

Topics in number theory 
Riemann surfaces 

MA2 
Topics in algebraic geometry 
Introduction to Riemannian geometry 
Linear algebraic groups 
Modular forms and applications 
Homotopical algebra 
Linear algebraic groups 
Complex manifolds 
Representation theory of semisimple Lie algebras 
padic numbers and applications 

Complex manifolds 
Ergodic theory and its applications to number theory 
Algebraic Ktheory 

Topics in arithmetic geometry 
Introduction to General Relativity 
Topics in number theory 
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 and Geometric Group Theory  Prof. Nicolas Monod 
Number Theory  Prof. Maryna Viazovska 
Reductive Groups  Prof. Donna Testermann 
Topology  Prof. Kahtryn Hess Bellwald 
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
 combinatorics track
 probability track