Due to the COVID-19 crisis, the information below is subject to change,
in particular that concerning the teaching mode (presential, distance or in a comodal or hybrid format).
5 credits
30.0 h + 15.0 h
Q1
This biannual learning unit is not being organized in 2020-2021 !
Teacher(s)
Caprace Pierre-Emmanuel;
Language
French
Main themes
Aims
At the end of this learning unit, the student is able to : | |
| 1 | |
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.
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
Due to the COVID-19 crisis, the information in this section is particularly likely to change.
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
Due to the COVID-19 crisis, the information in this section is particularly likely to change.
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.
Other information
This biennial course is not taught during the academic year 2020-2021.
Online resources
Moodle:
https://moodleucl.uclouvain.be/
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.
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
MATH
