After successful completion of the course, students are able to prepare an advanced topic with connections to the theory of smooth mannifolds. They are able to present the content in written form and in front of an audience of their peers.

Topics from differential geometry that are beyond the scope of the lecture "104.276 AKANA Analysis on manifolds". For example:

• de Rham cohomology, de Rham theorem, Poincaré duality,...
• riemannian metric, connection, geodesics, Hopf-Rinow theorem,...
• (semi-)riemannian geometry, curvature,...
• symplectic manifolds,...

Students prepare a subject.

The grade is determined by the presentation and the extended written summary.