Klaus Kröncke: Differential geometry

First meeting: Thursday September 10, 2026 at 15.15 in room 3721 at the Department of Mathematics, KTH.

Teachers: Klaus Kröncke

Prerequisites: Knowledge of linear algebra and analysis in several variables as well as basic knowledge in topology and very basic knowledge of functional analysis

Content: In this course, we will first discuss the foundations of differential and Riemannian geometry, which includes the foundations of manifold theory, Riemannian metrics and geodesics. We will introduce some notions of curvature and study how curvature properties affect the global topology of the manifold. Furthermore, we will discuss the analysis of differential operators on manifolds, which includes spectral theory and applications in geometry and topology.