Time and place

Lecture: Di, Do, 8-10h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined and announced in class

The requirements for examinations, assessments and coursework are set out in the latest updates to the module handbooks, which will be published from the end of October as part of the annotated course catalogue.

Teaching

Teacher: Nadine Große
Assistant: Jonah Reuß
Language: in English

Content

Differential geometry investigates geometric properties of curved spaces using methods of differential calculus. It has applications in other areas of mathematics and in physics, such as theoretical mechanics and the theory of relativity.

This lecture provides an introduction to (semi-)Riemannian geometry. In particular, it will focus on geodesics and the Riemannian curvature tensor.

Previous knowledge

Required: Analysis~I–III, Lineare Algebra~I and II \ Prior exposure to curves and surfaces (“Kurven und Flächen”) and topology is beneficial.

Usability

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

Time and place

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

Teaching

Teacher: Nadine Große
Assistant: Jonah Reuß
Language: in English if requested, otherwise in German

Content

Eigenvalues of geometric differential operators play a central role in Riemannian geometry, linking analytic, geometric, and topological properties of manifolds. In this lecture we give an introduction to spectral theory on Riemannian manifolds, with particular emphasis on the Laplace–Beltrami operator. Some results from spectral theory and functional analysis will necessarily be taken as black boxes. We discuss fundamental results on eigenvalue estimates and their dependence on the Riemannian metric. Through classical examples and key inequalities (such as those due to Cheeger, Lichnerowicz, and Weyl), we illustrate how curvature, volume, and topology influence the spectrum.

Previous knowledge

Differential geometry I is required; knowledge of Riemannian metrics and integration on manifolds is desirable.

Usability

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

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Time and place

Seminar: Di, 12-14h, SR 125, Ernst-Zermelo-Str. 1
Preliminary seminar meeting 03.02., 12:00, SR 318, Ernst-Zermelo-Str. 1
Individual preparation meetings for the talks: Dates by arrangement

Teaching

Teacher: Nadine Große
Assistant: Maximilian Stegemeyer
Language: Talk/participation possible in German and English

Content

Algebraic topology studies how topological spaces can be assigned algebraic objects, such as homology and cohomology groups. The homology and cohomology of a compact manifold have a special property that other spaces generally do not fulfil. The homology and cohomology of a compact manifold together satisfy what is known as Poincaré duality. This special structure has many interesting consequences; for example, there is now a product on the homology groups, the intersection product. In this seminar, we will first learn about the algebraic topology of manifolds and study Poincaré duality and the intersection product. The ideas behind the intersection product can then be transferred to the free loop space of a manifold. The homology of the free loop space thus also obtains a product, as well as other algebraic structures. The study of these additional algebraic structures on the loop space is called string topology. In this seminar, we will learn about some aspects and applications of string topology and finally see what string topology can tell us about the geometry and topology of the underlying manifold.

Previous knowledge

Algebraic topology, in particular basic knowledge of singular homology and cohomology. Other courses, such as Differential Geometry I, are helpful but not a prerequisite for participation in the seminar.

Usability

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

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Time and place

Lecture: Mi, 10-12h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours, various dates
Sit-in exam 29.07., 08:30-11:30, HS Rundbau, Albertstr. 21
Sit-in exam (resit) 08.10., 08:30-11:30, HS Weismann-Haus, Albertstr. 21a

Teaching

Teacher: Nadine Große
Assistant: Jonah Reuß
Language: in German

Content

The lecture gives an introduction to elementary geometry in Euclidian and non-Euclidian space and its mathematical foundations. We get to know Euclidean, hyperbolic, and projective geometry as examples of incidence geometries, and study their symmetry groups.

The next main topic is the axiomatic characterization of the Euclidean plane. The focus is on the story of the fifth Euclidian axiom (and the attempts to get rid of it).

Previous knowledge

Linear Algebra I

Usability

Elementary Geometry (2HfB21, MEH21, MEB21, MEdual24)
Compulsory Elective in Mathematics (BSc21)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Time and place

Seminar: Di, 12-14h, SR 226, Hermann-Herder-Str. 10
Preliminary seminar meeting 04.02., 10:00, SR 318, Ernst-Zermelo-Str. 1
Individual preparation meetings for the talks: Dates by arrangement

Teaching

Teacher: Nadine Große
Assistant: Maximilian Stegemeyer
Language: Talk/participation possible in German and English

Previous knowledge

Differential Geometry I

Usability

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

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

30.09.–02.10. and 04.10.; begins on 30.09. at 9h15 in HS Rundbau.

Teaching

Teacher: Nadine Große
Assistant: Jonah Reuß
Language: in German

Time and place

Lecture: Mi, 8-10h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours, various dates
Sit-in exam 12.02., 08:30-11:30, GHS Chemie (HS -1028), Flachbau Chemie, Albertstr. 21
Sit-in exam (resit) 09.04., 08:30-11:30, HS II, Albertstr. 23b

Teaching

Teacher: Nadine Große
Assistant: Jonah Reuß
Language: in German

Content

\textit{Multiple integration:} Jordan content in \(\mathbb R^n\), Fubini's theorem, transformation theorem, divergence and rotation of vector fields, path and surface integrals in \(\mathbb R^3\), Gauss' theorem, Stokes' theorem.\ \textit{Complex analysis:} Introduction to the theory of holomorphic functions, Cauchy's integral theorem, Cauchy's integral formula and applications.

Previous knowledge

Required: Analysis~I and II, Linear Algebra~I and II

Usability

Further Chapters in Analysis (MEd18, MEH21, MEdual24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Time and place

Lecture: Mi, 10-12h, HS Weismann-Haus, Albertstr. 21a
Sit-in exam (resit) 10.02., 08:30-11:30, HS Weismann-Haus, Albertstr. 21a

Teaching

Teacher: Nadine Große
Assistant: Marius Amann

Usability

Compulsory Elective in Mathematics (BSc21)
Elementary Geometry (2HfB21, MEH21, MEB21, MEdual24)

Time and place

Lecture: Di, Do, 10-12h, SR 404, Ernst-Zermelo-Str. 1

Teaching

Teacher: Nadine Große
Assistant: Jonah Reuß

Time and place

Mo, 16-18h, SR 125, Ernst-Zermelo-Str. 1

Teaching

Teacher: Sebastian Goette, Nadine Große, Christian Ketterer

Time and place

Do, 15-16h, HS II, Albertstr. 23b

Teaching

Teacher: Nadine Große, Amador Martín Pizarro

Time and place

Lecture: Mi, 8-10h, HS II, Albertstr. 23b
Sit-in exam 14.02., 08:30-11:30
Sit-in exam (resit) 10.04., 08:30-11:30

Teaching

Teacher: Nadine Große
Assistant: Marius Amann
general:

Usability

Further Chapters in Analysis (MEd18, MEH21, MEdual24)

Time and place

Lecture: Di, Do, 10-12h, HS II, Albertstr. 23b

Teaching

Teacher: Nadine Große
Assistant: Maximilian Stegemeyer
general:

Usability

Compulsory Elective in Mathematics (BSc21)

Time and place

Mo, 16-18h, SR 404, Ernst-Zermelo-Str. 1

Teaching

Teacher: Sebastian Goette, Nadine Große, Christian Ketterer

Time and place

Do, 15-16h, HS II, Albertstr. 23b

Teaching

Teacher: Amador Martín Pizarro, Nadine Große

Time and place

Lecture: Di, Do, 10-12h, HS II, Albertstr. 23b

Teaching

Teacher: Nadine Große
Assistant: Marius Amann
general:

Time and place

Do, 12-14h, SR 125, Ernst-Zermelo-Str. 1

Teaching

Teacher: Nadine Große
Assistant: Coffi Aristide Hounkpe, Jakob Rotter

Time and place

Di, 12-14h, SR 404, Ernst-Zermelo-Str. 1

Teaching

Teacher: Nadine Große, Jonas Schnitzer
Assistant: Nadine Große, Jonas Schnitzer

Time and place

Mo, 16-18h, SR 125, Ernst-Zermelo-Str. 1

Teaching

Teacher: Sebastian Goette, Nadine Große

Time and place

Lecture: Mi, 8-10h, HS Weismann-Haus, Albertstr. 21a
Sit-in exam 21.02., 13:00-16:00
Sit-in exam (resit) 13.05., 08:30-11:30

Teaching

Teacher: Nadine Große
Assistant: Ksenia Fedosova
general:

Usability

Further Chapters in Analysis (MEd18, MEH21, MEdual24)

Time and place

Di, 12-14h, SR 404, Ernst-Zermelo-Str. 1

Teaching

Teacher: Nadine Große
Assistant: Ksenia Fedosova

Usability

Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)

Time and place

Mo, 16-18h, HS II, Albertstr. 23b

Teaching

Teacher: Sebastian Goette, Nadine Große, Christian Ketterer

Time and place

Lecture: Di, Do, 10-12h, HS II, Albertstr. 23b
Sit-in exam 06.09., 08:00-12:00
Sit-in exam (resit) 15.02., 09:00-12:00

Teaching

Teacher: Nadine Große
Assistant: Marius Amann
general:

Usability

Mathematical Specialisation (MEd18, MEH21)
Compulsory Elective in Mathematics (BSc21)
Pure Mathematics (MSc14)
Applied Mathematics (MSc14)

Time and place

Mo, 14-16h, SR 127, Ernst-Zermelo-Str. 1

Teaching

Teacher: Sebastian Goette, Nadine Große
Assistant: Mara Ungureanu

Usability

Supplementary Module in Mathematics (MEd18)
Compulsory Elective in Mathematics (BSc21)

Time and place

Mo, 16-18h, SR 125, Ernst-Zermelo-Str. 1

Teaching

Teacher: Sebastian Goette, Nadine Große, Christian Ketterer

Time and place

Mi, 14-16h, SR 226, Hermann-Herder-Str. 10

Teaching

Teacher: Sebastian Goette, Nadine Große, Annette Huber-Klawitter, Stefan Kebekus, Wolfgang Soergel
Assistant: Vivien Vogelmann

Time and place

Lecture: Di, Do, 10-12h, HS 01 007, Hermann-Herder-Str. 6

Teaching

Teacher: Nadine Große
Assistant: Ksenia Fedosova
general:

Usability

Mathematical Specialisation (MEd18, MEH21)
Analysis III (BSc21)

Teaching

Teacher: Nadine Große
Assistant: Ksenia Fedosova

Time and place

Mi, 14-16h, HS II, Albertstr. 23b

Teaching

Teacher: Sebastian Goette, Nadine Große, Annette Huber-Klawitter, Stefan Kebekus

Time and place

Mo, 16-18h, HS II, Albertstr. 23b

Teaching

Teacher: Nadine Große, Sebastian Goette

Time and place

Mo 8-10h, HS Weismann-Haus, Albertstr. 21a, 10-12h, HS Weismann-Haus, Albertstr. 21a
Mo 12-14h, HS Weismann-Haus, Albertstr. 21a, 14-16h, HS Weismann-Haus, Albertstr. 21a
Mo 16-18h, HS Weismann-Haus, Albertstr. 21a, Di, 10-12h, HS Weismann-Haus, Albertstr. 21a
Di 12-14h, HS Weismann-Haus, Albertstr. 21a, 14-16h, HS Weismann-Haus, Albertstr. 21a
Mi, 8-10h, HS Weismann-Haus, Albertstr. 21a
Q&A session: Di, 8-10h, , online
Sit-in exam 06.09., 09:00-13:00
Sit-in exam (resit) 14.02., 09:00-13:00

Teaching

Teacher: Nadine Große
Assistant: Ksenia Fedosova
general: ,

Usability

Analysis II (BScInfo, BScPhys)

Time and place

Di, 12-14h, HS II, Albertstr. 23b

Teaching

Teacher: Nadine Große
Assistant: Ksenia Fedosova

Usability

Introductory Student Seminar (2HfB21, BSc21, MEH21, MEB21)

Time and place

Mo, 16-18h, bbb-Raum "Anderssen", online

Teaching

Teacher: Sebastian Goette, Nadine Große, Katrin Wendland

Time and place

Mi Do, 14-16h, bbb-Raum des Graduiertenkollegs, online

Teaching

Teacher: Andriy Haydys, Annette Huber-Klawitter, Fritz Hörmann, Stefan Kebekus, Sebastian Goette, Nadine Große, Wolfgang Soergel, Katrin Wendland
Assistant: Jonas Schnitzer

Time and place

Q&A session: Mi, 8-10h, , online
Sit-in exam 25.03., 09:00-13:00
Sit-in exam 26.07., 09:00-13:00

Teaching

Teacher: Nadine Große
Assistant: Ksenia Fedosova
general: ,

Time and place

Mi 14-16h, SR 125, Ernst-Zermelo-Str. 1, Do, 14-16h, bbb-Raum "Krush", online

Teaching

Teacher: Nadine Große, Andriy Haydys, Annette Huber-Klawitter, Wolfgang Soergel, Stefan Kebekus, Katrin Wendland

Time and place

Mo, 16-18h, bbb-Raum "Kasparov", online

Teaching

Teacher: Katrin Wendland, Nadine Große

Time and place

Fr, 14-17h, wechselnder Hörsaal, -

Teaching

Teacher: Andreas Buchleitner, Nadine Große, Wolfgang Soergel, Katrin Wendland

Time and place

Lecture: Mo, Mi, 10-12h, HS II, Albertstr. 23b

Teaching

Teacher: Nadine Große
Assistant: Ksenia Fedosova
general:

Usability

Compulsory Elective in Mathematics (BSc21)

Time and place

Mo, 16-18h, SR 404, Ernst-Zermelo-Str. 1

Teaching

Teacher: Sebastian Goette, Nadine Große, Katrin Wendland

Time and place

Mi, 14-16h, SR 404, Ernst-Zermelo-Str. 1

Teaching

Teacher: Sebastian Goette, Nadine Große, Andriy Haydys, Stefan Kebekus, Wolfgang Soergel, Katrin Wendland

Time and place

Fr, 14-17h, wechselnder Hörsaal, -

Teaching

Teacher: Andreas Buchleitner, Sebastian Goette, Nadine Große, Wolfgang Soergel, Katrin Wendland

Time and place

Lecture: Mo, 14-16h, HS Weismann-Haus, Albertstr. 21a, Mi, 12-14h, SR 404, Ernst-Zermelo-Str. 1

Teaching

Teacher: Nadine Große
Assistant: Ksenia Fedosova
general:

Usability

Compulsory Elective in Mathematics (BSc21)

Time and place

Mi, 14-16h, SR 404, Ernst-Zermelo-Str. 1

Teaching

Teacher: Sebastian Goette, Nadine Große, Andriy Haydys, Annette Huber-Klawitter, Wolfgang Soergel, Katrin Wendland, Stefan Kebekus

Time and place

Mo, 16-18h, SR 404, Ernst-Zermelo-Str. 1

Teaching

Teacher: Sebastian Goette, Nadine Große, Katrin Wendland

Time and place

Fr, 14-17h, wechselnder Hörsaal, -

Teaching

Teacher: Andreas Buchleitner, Sebastian Goette, Nadine Große, Wolfgang Soergel, Katrin Wendland

Time and place

Mi, 10-12h, SR 125, Ernst-Zermelo-Str. 1

Teaching

Teacher: Nadine Große
Assistant: Ksenia Fedosova

Usability

Introductory Student Seminar (2HfB21, BSc21, MEH21, MEB21)

Time and place

Mo, 14-16h, SR 125, Ernst-Zermelo-Str. 1

Teaching

Teacher: Andriy Haydys, Sebastian Goette
Assistant: Sebastian Goette, Nadine Große

Usability

Compulsory Elective in Mathematics (BSc21)

Time and place

Mo, 16-18h, SR 404, Ernst-Zermelo-Str. 1

Teaching

Teacher: Sebastian Goette, Nadine Große, Katrin Wendland

Time and place

Mi 14-16h, SR 404, Ernst-Zermelo-Str. 1, Di, 12-14h, SR 218, Ernst-Zermelo-Str. 1

Teaching

Teacher: Sebastian Goette, Nadine Große, Annette Huber-Klawitter, Andriy Haydys, Wolfgang Soergel, Katrin Wendland

Time and place

Fr, 14-17h, wechselnder Hörsaal, -

Teaching

Teacher: Andreas Buchleitner, Sebastian Goette, Nadine Große, Wolfgang Soergel, Katrin Wendland

Time and place

Lecture: Mo, Mi, 10-12h, SR 404, Ernst-Zermelo-Str. 1

Teaching

Teacher: Nadine Große
Assistant: Ksenia Fedosova
general:

Usability

Compulsory Elective in Mathematics (BSc21)

Time and place

Mi, 12-14h, SR 125, Ernst-Zermelo-Str. 1

Teaching

Teacher: Nadine Große
Assistant: Ksenia Fedosova

Usability

Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)

Time and place

Mo, 16-18h, SR 404, Ernst-Zermelo-Str. 1

Teaching

Teacher: Sebastian Goette, Nadine Große, Katrin Wendland

Time and place

Mi, 14-16h, SR 404, Ernst-Zermelo-Str. 1

Teaching

Teacher: Sebastian Goette, Nadine Große, Andriy Haydys, Annette Huber-Klawitter, Fritz Hörmann, Stefan Kebekus, Wolfgang Soergel, Katrin Wendland

Time and place

Fr, 14-17h, wechselnder Hörsaal, -

Teaching

Teacher: Andreas Buchleitner, Sebastian Goette, Nadine Große, Emmanuel Scheidegger, Wolfgang Soergel, Katrin Wendland