MATH-F511: Global Analysis

2025-26

Time and Room: usually on Fridays, 10:00-12:00 in Forum I.2080.

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: 13 FEB 2026).

Literature

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