Course starts Thursday 24. April

Responsible: Rudolf Zeidler

Plan of the lecture course:
The scalar curvature is in some sense the simplest differential-geometric curvature quantity for a Riemannian manifold. However, while for (2-dimensional) surfaces it agrees with the classical Gaussian curvature, its concrete geometric meaning in higher dimensions is notoriously hard to grasp.

Nevertheless, the geometry of scalar curvature has been an exciting topic for a long time, in particular in the context of the positive mass theorem in mathematical general relativity. This theorem asserts, loosely speaking, that the total gravitational energy of an isolated system is nonnegative. From a mathematical perspective, this is closely related to a result in scalar curvature geometry asserting that the (3-dimensional) torus cannot be endowed with a Riemannian metric of positive scalar curvature.More recently, in the last few years new consequences of lower scalar curvature bounds such as distance inequalities have been discovered in the spirit of classical comparison geometry. 

In this lecture course, I will give a gentle introduction to these topics, primarily in the 3-dimensional case, using an approach to scalar curvature geometry via harmonic functions. As prerequisite to follow this course, a first course in differential geometry (including smooth manifolds, tangent spaces, basic definition of Riemannian curvature) will suffice.

Schedule:
Lecture: Tuesday, 16:15-17:45
Lecture/Tutorial: Thursday, 8:15-9:45

Place: Institute for Mathematics, Campus Golm, House 9:
Lecture (Tuesday): Room 2.09.1.10
Lecture/Tutorial (Thursday): Room 2.09.0.14 

Moodle: Please register here