Metric geometry (Summer Semester 2023)
- Lecturer: Dr. Artem Nepechiy
- Classes: Lecture (0171600), Problem class (0171610)
- Weekly hours: 4+2
| Schedule | ||
|---|---|---|
| Lecture: | Tuesday 15:45-17:15 | 20.30 SR 2.067 |
| Wednesday 8:00-9:30 | 20.30 SR 2.066 | |
| Problem class: | Friday 8:00-9:30 | 20.30 SR 3.061 |
| Lecturers | ||
|---|---|---|
| Lecturer, Problem classes | Dr. Artem Nepechiy | |
| Office hours: by appointment | ||
| Room 1.004 Kollegiengebäude Mathematik (20.30) | ||
| Email: artem.nepechiy@kit.edu | Problem classes | Dr. David Degen |
| Office hours: | ||
| Room 1.021 Kollegiengebäude Mathematik (20.30) | ||
| Email: david.degen@kit.edu | ||
The overall goal is to develop a better understanding of Riemannian manifolds - or other geometric objects. One possible approach is to conceive of them as metric spaces and to study the associated distance functions.
Here, properties of distance functions are reflected in global invariants. For example, if all distance functions of a Riemannian manifold are more concave than in the plane, this results in the global sectional curvature bound
.
This idea can also be iterated. In this case, one now searches for a metric space containing the set of all isometry classes of Riemannian manifolds and studies it.
This approach has proved to be very fruitful in the past decades and has allowed to bring to light many important results in differential geometry and topology.
The topics covered in the lecture are:
- Convergence of metric spaces
- Comparison geometry
- Curvature-free geometry of manifolds
The lecture will follow the script of Anton Petrunin: Lectures on metric geometry
Prerequisites:
Basic knowledge of set-theoretic topology. Very helpful would be already existing
knowledge of a geometry lecture and knowledge of fundamental groups.