Algebra and Geometry track

(last modified 09.06.2020)

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:

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"). Nevertheless 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 

non-positive 

curvature 

and groups

Combinatorial 

number

theory

BA6

Algebraic

curves

 

Representation

theory

Algebraic

number

theory

Algebraic 

topology

Representation

theory of finite

groups

MA1

Modern

algebraic

geometry

Riemann 

surfaces

Analysis on

groups

Automorphic

forms and

L-functions

Homotopy 

theory

Algebraic 

K-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

p-adic

numbers and

applications

Complex

manifolds

Ergodic 

theory

and its

applications

to 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 :