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Dirac operators on manifolds with boundary

Course Type: 
PhD Course
Academic Year: 
Jan - Mar
20 h
This is an introductory course on the analysis of Dirac operators on manifolds with boundary. Our goal is to prepare the background to deal with a number of applications of elliptic boundary value problems for Dirac operators which are frequently encountered in Geometry and in Mathematical Physics.
The first part of the course will focus on the general theory of elliptic boundary value problems. We will discuss Dirac-type operators, boundary conditions (local and global), ellipticity of boundary conditions, Fredholmness of the realisations, and some general index theorems. 
In the second part of the course we will illustrate the Atiyah-Patodi-Singer index formula and the eta-invariant, discussing as an application the signature formula for a manifold with boundary.
The course will mostly follow the paper: 
C. Bär, W. Ballmann, "Guide to elliptic boundary value problems for Dirac-type operators". Arbeitstagung Bonn 2013, 43–80, Progr. Math., 319, Birkhäuser/Springer, Cham, 2016


Additional Material: 
The first two lectures will be held in A-134, the following ones will be held in A-136

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