MAU34304 Groups and geometry
| Module Code | MAU34304 |
|---|---|
| Module Title | Groups and geometry |
| Semester taught | Semester 2 |
| ECTS Credits | 5 |
| Module Lecturer | Prof. Tommaso Cremaschi |
| Module Prerequisites |
MAU11100 Linear algebra and
MAU22101 Group theory and MAU23203 Analysis in several real variables |
Assessment Details
- This module is examined in a 2-hour examination at the end of Semester 2.
- Continuous assessment contributes 10% towards the overall mark.
- The module is passed if the overall mark for the module is 40% or more. If the overall mark for the module is less than 40% and there is no possibility of compensation, the module will be reassessed as follows:
1) A failed exam in combination with passed continuous assessment will be reassessed by an exam in the supplemental session;
2) The combination of a failed exam and failed continuous assessment is reassessed by the supplemental exam;
3) A failed continuous assessment in combination with a passed exam will be reassessed by one or more summer assignments in advance of the supplemental session.Capping of reassessments applies to Theoretical Physics (TR035) students enrolled in this module. See full text at https://www.tcd.ie/teaching-learning/academic-affairs/ug-prog-award-regs/derogations/by-school.php Select the year and scroll to the School of Physics.
Contact Hours
11 weeks of teaching with 3 lectures per week.
Learning Outcomes
On successful completion of this module, students will be able to
- Apply basic theorems on discrete subgroups of isometries.
- Build examples of discrete groups acting on different geometric spaces.
- Classify wallpaper groups.
Module Content
The aim of this module is to study the isometry groups of various metric spaces such as real euclidean n-space, spherical n-space, and hyperbolic n-space with an emphasis on their discrete subgroups. As an example of topics, we will look at crystallographic/wallpaper groups, Bieberbach theorem, Schottky groups and the ping-pong Lemma.