Lecturer: Prof. Dr. Petra Schwer
Teaching assistants: Dr. José Pedro Quintanilha, Bianca Marchionna
Links: heiCO (lecture), heiCO (exercise class), Müsli

This lecture is classified as a "Grundmodul".

Weekly schedule

Lectures: Wednesday 09:15 - 10:45 in SR 4, Friday 09:15 - 10:45 in SR 3
Exercise classes: Monday 09:15 - 10:45 in SR 3

Each week on Friday, an exercise sheet will be published, which is to be handed in on the following Friday, and will be discussed in the ensuing exercise class on Monday. In the first week there will be no exercise class, and in the second week we will have in-class exercises.

Evaluation

Evaluation is through an oral examination at the end of the semester. Here are the evaluation criteria: Bewertungskriterien für mündliche Prüfungen.

Attendance of the lectures and exercise classes, as well as homework submission, are optional. Students are however encouraged to work on the problem sheets and submit their work individually or in groups, and to present their solutions in class. Homework can be submitted by e-mail to jquintanilha [at] mathi [dot] uni-heidelberg [dot] de.

Program

In geometric group theory, we study the interactions between groups and geometry. The goal is to investigate groups with the help of geometric tools. To that end, we endow them with a metric, or consider their actions on suitable metric spaces. The techniques are thus often rich in visual imagery. The following quote conveys the flavor of the subject:

We often think by analogies. We have pictures in small dimensions and must try to decide how much of the picture remains accurate in higher dimensions and how much has to change. This visualization is very different from just manipulating a string of symbols.

(John Milnor, 2011)

Pre-requisites: Basic group theory and linear algebra.
Problem sheet 0 (in-class exercises)

Literature

It will not be necessary to consult literature beyond the lecture notes in order successfully take part in the course. Nevertheless, here are some additional resources: