Lecture: Di, Do, 10-12h, SR 404, Ernst-Zermelo-Str. 1
Exercise session: Mi, 14-16h, SR 403, Ernst-Zermelo-Str. 1
Requirements on examinations, assessments and coursework will be described in the supplements of the module handbooks to be published as part of the course cataloque by end of October.
Teacher: Maximilian Stegemeyer
Language: in German
Algebraic topology studies topological spaces by assigning algebraic objects, e.g. groups, vector spaces or rings, to them in a particular way. This assignment is usually done in a way which is invariant under homotopy equivalences. Therefore one often speaks of homotopy invariants and algebraic topology can be seen as the study of the construction and the properties of homotopy invariants.
In this lecture we will first recall the notion of the fundamental group of a space and study its connection to covering spaces. Then we will introduce the singular homology of a topological space and study it extensively. In the end, we will consider cohomology and homotopy groups and explore their relation to singular homology. We will also consider various applications of these invariants to topological and geometric problems.
Topology
Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Mathematical Concentration (MEd18, MEH21)
Pure Mathematics (MSc14)
Mathematics (MSc14)
Concentration Module (MSc14)
Elective (MSc14)
Elective (MScData24)
Lecture: Mo, Mi, 8-10h, HS Rundbau, Albertstr. 21
Tutorial: 2 hours, various dates
Teacher: Michael Růžička
Assistant: Maximilian Stegemeyer
Language: in German
Analysis II is the continuation of Analysis I from the winter semester and one of the basic lectures of the study programmes in Mathematics. Central concepts of Analysis I (limits and derivations) will be generalized to the case of higher dimension.
Central topics are the topology of \(\mathbb R^n\), metrics and norms, differential calculs in several variables, ordinary differential equations and in particular linear differential equations.
Analysis I, Linear Algebra I (or bridge course linear algebra)
Analysis (2HfB21, BSc21, MEH21, MEB21)
Analysis II (BScInfo19, BScPhys20)
Seminar: Di, 12-14h, SR 226, Hermann-Herder-Str. 10
Preliminary Meeting 04.02., 10:00, SR 318, Ernst-Zermelo-Str. 1
Preparation meetings for talks: Dates by arrangement
Teacher: Nadine Große
Assistant: Maximilian Stegemeyer
Language: Talk/participation possible in German and English
Differential Geometry I
Elective (Option Area) (2HfB21)
Mathematical Seminar (BSc21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Mathematical Seminar (MSc14)
Elective (MSc14)
Elective (MScData24)
Lecture: Do, 14-16h, SR 404, Ernst-Zermelo-Str. 1
Exercise session: Di, 8-10h, SR 127, Ernst-Zermelo-Str. 1
Teacher: Maximilian Stegemeyer
Language: in English
Lie groups and operations of Lie groups play a central role in geometry and topology. They can be used to describe continuous symmetries, one of the most important concepts of mathematics and physics. Exploiting symmetries, e.g. when describing homogeneous spaces, makes it easier to solve many specific problems and often provides a deeper insight into the structures examined. In addition, the geometry and topology of Lie groups and homogeneous spaces is of great interest.
In this lecture, we start with introducing the basic theory of Lie groups and Lie algebras, especially with insights into the structure theory of Lie algebras. In the second part we will look at homogeneous spaces with a special focus on Riemannian symmetric spaces. The latter form an important class of examples of Riemannian manifolds. In addition to the Lie-theoretical aspects, a special focus will always be on the homogeneous Riemannian metrics of the respective spaces.
Required: Differential geometry~I
Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Pure Mathematics (MSc14)
Mathematics (MSc14)
Concentration Module (MSc14)
Elective (MSc14)
Elective (MScData24)
Lecture: Di, Do, 10-12h, HS II, Albertstr. 23b
Teacher: Nadine Große
Assistant: Maximilian Stegemeyer
general:
Compulsory Elective in Mathematics (BSc21)