Time and place

Lecture: Di, Do, 10-12h, SR 404, Ernst-Zermelo-Str. 1
Tutorial: 2 hours, date to be determined

Teacher: Maximilian Stegemeyer
Language: in German

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)

Time and place

Lecture: Mo, Mi, 12-14h, SR 404, Ernst-Zermelo-Str. 1
Tutorial: 2 hours, date to be determined

Teacher: Guofang Wang
Assistant: Xuwen Zhang
Language: in German

In the lecture, we discuss the geometry of the sub-manifolds of Euclidian spaces. Examples of such sub-manifolds are curves in the plane and surfaces in the 3-dimensional space. In the 1st part we introduce the external geometry of the sub-manifold, e.g. the second fundamental form, the mean curvature, the first variation of the area, the equations of Gauss, Codazzi and Ricci. In the 2nd part we examine tminimal hypersurfaces (minimal surfaces), the hypersurface with constant mean curvature and the geometric inequalities, the isoperimetric inequality and its generalisations.

Analysis III and "Differential Geometry" or "Curves and Surfaces"

Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Pure Mathematics (MSc14)
Mathematics (MSc14)
Concentration Module (MSc14)
Elective (MSc14)
Elective (MScData24)

Time and place

Lecture: Di, Do, 10-12h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined
22.07.
Sit-in exam (resit) 13.10.

Teacher: Heike Mildenberger
Assistant: Hannes Jakob
Language: in German

A topological space consists of a basic set \(X\) and a family of open subsets of the basic set, which is called topology on \(X\). Examples over the basic sets \(\mathbb R\) and \({\mathbb R}^n\) are given in the analysis lectures. The mathematical subject \glqq{}Topology\grqq\ is the study of topological spaces and the investigation of topological spaces. Our lecture is an introduction to set-theoretic and algebraic topology.

Analysis I and II, Linear Algebra I

Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Mathematical Concentration (MEd18, MEH21)
Pure Mathematics (MSc14)
Elective (MSc14)
Elective (MScData24)

Time and place

Lecture: Mo, 14-16h, SR 404, Ernst-Zermelo-Str. 1
Tutorial: 2 hours, date to be determined

Teacher: Mikhail Tëmkin
Language: in English

The notion of a manifold is fundamental importance. On one hand, it is a common ground for many branches of pure and applied mathematics, as well as mathematical physics. On the other hand, it itself is a lush source of elegant, unexpected and structural results. Next, algebraic topology is to mathematics what the periodic table is to chemistry: it offers order to what seems to be chaotic (more precisely, to topological spaces of which manifolds is an important example). Finally, differential topology studies smooth manifolds using topological tools. As it turns out, narrowing the scope to manifolds provides many new beautiful methods, structure and strong results, that are applicable elsewhere -- as we will see in the course. Necessary notions from algebraic topology will be covered in the beginning.

Point-set topology (e.g. "Topology" from summer semester of 2024)

Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Pure Mathematics (MSc14)
Mathematics (MSc14)
Concentration Module (MSc14)
Elective (MSc14)
Elective (MScData24)

Time and place

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)

Time and place

Lecture: Mo, Mi, 14-16h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined

Teacher: Sebastian Goette
Assistant: Mikhail Tëmkin
Language: in German

Differential geometry, especially Riemannian geometry, deals with the geometric properties of curved spaces. Such spaces also occur in other areas of mathematics and physics, for example in geometric analysis, theoretical mechanics and the general theory of relativity.

Required: Analysis~I–III, Lineare Algebra~I and II \ Recommended: Analysis of Curves and Surfaces ("Kurven und Flächen"), 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)

Time and place

Lecture: Di, 16-18h, SR 403, Ernst-Zermelo-Str. 1

Teacher: Wolfgang Soergel
Language: in German

Introduction to classic mechanics from the point of view of mathematics. We start with the mathematical modelling of space and time. Then we discuss Newton's equations of movement, physical systems with compulsory conditions, the D'Alembert principle, the Hamilton formalism and its derivation from the Newton's equations and applications of Hamilton formalism.

Required: Analysis III

Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Elective (BSc21)
Supplementary Module in Mathematics (MEd18)

Time and place

Seminar: Di, 14-16h, SR 125, Ernst-Zermelo-Str. 1
Preliminary Meeting 16.07., SR 125, Ernst-Zermelo-Str. 1
Preparation meetings for talks: Dates by arrangement

Teacher: Sebastian Goette
Assistant: Mikhail Tëmkin
Language: Talk/participation possible in German and English

We will discuss advanced topics in algebraic topology. Depending on the interest of the participants we could work on one of the following topics---if you have other topic suggestions, please contact the lecturer.

• The Steenrod algebra. An additional structure on the cohomology modulo \(p\) allows finer statements on the existence of continuous mappings, such as the existence of of linearly independent vector fields on spheres. The Wu formulas provide a connection to characteristic classes of manifolds.
• Structured spectra. In order to represent multiplicative (co-)homology functors by spectra, one needs a closed monoidal category of spectra, for example a category of spectra, for example symmetric or orthogonal spectra. In this context we also get to know model structures better.
• \(K\)-theory and index theory. Elliptic differential operators on compact manifolds are manifolds are Fredholm operators. Their index can be defined by the theorem of Atiyah--Singer topologically. We prove this theorem using (mainly) topological methods and give some geometric applications.

Algebraic Topology~I and II

Elective (Option Area) (2HfB21)
Mathematical Seminar (BSc21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Mathematical Seminar (MSc14)
Elective (MSc14)
Elective (MScData24)