This course (in English) is an introduction in Metric Geometry. The target audience for this are students with a basic knowledge in geometry, discrete geometry and topology. In the course we will introduce and develop basic notions and methods of Metric Geometry following presentation from the book of Burago, Burago and Ivanov: “A course in Metric Geometry.” Here is the list of some chapters of the book, and thus (roughly) an outline of the course contents:
1. Metric Spaces
2. Length Spaces
4. Spaces of Bounded Curvature
5. Smooth Length Structures
6. Curvature of Riemannian Metrics
7. Spaces of Metric Spaces
1. Burago, Burago and Ivanov: “A course in Metric Geometry” (Graduate Studies in Mathematics Vol. 33; AMS)
Zielgruppe: The target audience are students with a solid background in discrete geometry and/or convex geometry (en par with Discrete Geometry I & II). The topic of this course is a state-of-the-art of advanced topics in discrete geometry that find applications and incarnations in differential geometry, topology, combinatorics, and algebraic geometry.
Voraussetzungen: Preferably Discrete Geometry I and II. Background in discrete geometry (polytopes, subdivisions, h-vectors) and convex geometry (mixed volumes, Brunn-Minkowski, Aleksandrov-Fenchel) should suffice.