Lecture “Selected Topics in differential geometry”, SoSe 2023

Prof. Dr. Joachim Lohkamp

Entry in the course catalog: Lecture / Tutorial

Mondays 12:30–14:00 in Room 311, Einsteinstr. 62 and Thursdays 16:15–17:45 in M6.

In this course we will focus on the geometry of Ricci and scalar curvature. We will introduce to techniques to understand what these curvatures mean and how they are related to the topology of the underlying spaces. We start with results for positive versus negative Ricci curvature. Then we will turn to scalar curvature, which has become one of the major subjects in current research during the past decade. Scalar curvature links many different areas in mathematics from topology, index theory, operator algebras, differential geometry to general relativity in mathematical physics. We will choose the subject depending on the interest and background of the audience.

Minimal prerequisites are a basic knowledge of manifolds and differential geometry as taught in the standard course “Differential Geometry 1” and it would be very nice (but not strictly necessary) if “Minimal Surfaces” are equally well-known.

Tutorial

Dr. Matthias Kemper

Friday 12:15–13:45 in room 304 ⅔  („Lichthof” on the third floor), Einsteinstr. 62.
First session on April 14.

Exercise sheet 1 (due on April 20)
Exercise sheet 2 (due on April 27)
Exercise sheet 3 (due on May 4)
Exercise sheet 4 (due on May 11)
Exercise sheet 5 (due on May 25)
Exercise sheet 6 (due on June 15)
Exercise sheet 7 (due on June 22)