MATH-F511: Global Analysis

2024

Time and Room: usually on Mondays, 10:00-12:00 in the Salle Debever.

Course content: The central topic of the course is the interplay between geometry, topology, and analysis. It turns out that elliptic differential operators on manifolds capture subtle information about the underlying space. For example, the dimension of the kernel of the Hodge Laplacian depends only on the topology of the underlying manifold. The aim of the course is to provide a glimpse in this exciting area of mathematics.

Lecture notes (Last updated: 16 JUN 2025).
Problems (Last updated: 05 MAR 2024).
An older list of problems (Last updated: 28 APR 2023). All problems appear in the newer list, this is left here for historical reasons.

Literature

F. Warner. Foundations of Differentiable Manifolds and Lie Groups.
R. Wells. Differential Analysis on Complex Manifolds.
A. Haydys. Introduction to gauge theory.