Groups theory

lmat2120  2019-2020  Louvain-la-Neuve

Groups theory
Note from June 29, 2020
Although we do not yet know how long the social distancing related to the Covid-19 pandemic will last, and regardless of the changes that had to be made in the evaluation of the June 2020 session in relation to what is provided for in this learning unit description, new learnig unit evaluation methods may still be adopted by the teachers; details of these methods have been - or will be - communicated to the students by the teachers, as soon as possible.
5 credits
30.0 h + 15.0 h
Q1

This biannual learning unit is being organized in 2019-2020
Language
French
Prerequisites


Main themes


Aims

At the end of this learning unit, the student is able to :

1

 

The contribution of this Teaching Unit to the development and command of the skills and learning outcomes of the programme(s) can be accessed at the end of this sheet, in the section entitled “Programmes/courses offering this Teaching Unit”.
Content
This course aims at introducing some of the fundamental concepts from the theory of groups. A special emphasis is put on finitely generated infinite groups, and their study by geometric methods.
The following themes will be discussed, starting from concrete examples.
  • Abelian, nilpotent and soluble groups.
  • Simple groups.
  • Free groups and groups acting on trees.
  • Gromov hyperbolic groups.
  • Linear groups and residual finiteness.
  • The Burnside Problem.
Teaching methods
The course is taught through lectures and practical exercises. In the practical exercise sessions, students will be asked to make suggestions and formulate ideas in order to further the course on the basis of their prior knowledge.
Evaluation methods
Assessment is by an examination during the exam session on one hand, and by projects during the semester on the other hand. The examination tests knowledge and understanding of fundamental concepts, examples and results, ability to construct a coherent argument, and mastery of the techniques of proof introduced during the course.
Online resources
Moodle:
https://moodleucl.uclouvain.be/
Bibliography
C. Drutu and M. Kapovich, Geometric Group Theory. American Mathematical Society Colloquium Publications 63, 2018.
P. de la Harpe, Topics in Geometric Group Theory. Chicago Lectures in Mathematics, 2000.
J. Meier, Groups, graphs and trees. An introduction to the geometry of infinite groups. London Mathematical Society Student Texts 73, Cambridge UP, 2008.
D. Robinson, A course in the theory of groups. (Second edition). Graduate Texts in Mathematics, Springer, 1996. 
J.-P. Serre, Arbres, amalgames, SL2. Astérisque, No. 46. Société Mathématique de France, Paris, 1977.
Teaching materials
  • matériel sur moodle
Faculty or entity


Programmes / formations proposant cette unité d'enseignement (UE)

Title of the programme
Sigle
Credits
Prerequisites
Aims
Master [120] in Mathematics

Master [60] in Mathematics