Pro-/Seminar on Algebra - Symmetries
- FU-Students should register via Campus Management.
- Non-FU-students should register via MyCampus/Whiteboard.
Summer Semester 2021
Lecturer: Dr. Gabriel Angelini-Knoll
Time and place: Wednesdays, 10:00-12:00 h, online
Criteria for proof of performance: a presentation and written summary
Target group: Students in the 3rd semester of mathematics.
Requirements: Only knowledge of some basic mathematical terms (group, vector space, linear mapping, metric, scalar product) is assumed. In addition to learning mathematical content, the goal of a proseminar is also to gain first experiences with scientific presentations in front of an audience.
Content: Symmetry is a phenomenon that plays a role in all natural sciences. Groups and the term group operation were invented to describe symmetries of mathematical objects. In this proseminar we will first examine the symmetries of figures in the plane and develop the basic mathematical terms "group" and "group operation", which are needed to describe symmetries. Later lectures will deal with groups with amazing properties.
Talk 1: Symmetry Motivation
|21.04.||Talk 2: Isometries of the plane||Jasper Seidensticker|
|28.04.||Talk 3: Classification of isometries of the plane||Hannah Schleupner|
|05.05.||Talk 4: Finite groups of motions of the plane||Emma Linn Stingele|
|12.05.||Talk 5: Discrete groups of motions of the plane, Part I||Urs Degendorfer|
|Talk 6: Discrete groups of motions of the plane, Part II||Eliza Baumann|
|19.05.||Talk 7: Group actions||Sebastian Schneider|
|26.05.||Talk 8: Group actions on cosets and counting formulas||Tianyi Hu|
|02.06.||Talk 9: Permutation representations||Taha Rayan|
|Talk 10: Finite subgroups of the rotation group||Lea Sophie Dohle|
|09.06.||Talk 11: Groups and Graphs||Luc Schoenmakers|
|16.06.||Talk 12: Cayley graphs||Kai Schweda|
|23.06.||Talk 13: Symmetries of Cayley graphs and fundamental domains||Mark Backhaus|
|Talk 14: Free groups and group presentations||Gerrit Charlotte Guddorf|
|30.06.||Talk 15: Free groups and graphs||Yannic Pascal Wendt|
|07.07.||Talk 16: Subgroups of free groups||Linus Dickert|
|14.07.||Talk 17: The group ℤ/ℤ3 ∗ ℤ/4ℤ||Florian Streckenbach|
- M. A. Armstrong. Groups and Symmetry. Undergraduate Texts in Mathematics. 1988.
- Michael Artin. Algebra. Birkhäuser Verlag, Basel, 1993.
- John Meier. Groups, graphs and trees. Cambridge University Press, Cambridge, 2008.
- Oleg Bogopolski. Introduction to group theory. European Mathematical Society (EMS), Zü̈rich, 2008.