Nonlinear Analysis 2
Nonlinear Analysis 2 in Summer term 2022
Professor Dr. Christof Melcher
Pontdriesch 14-16, Raum 214
The course is a continuation of Nonlinear Analysis 1 from the winter term 21/22. Contents from that lecture are assumed to be known.
The lecture will take place in person. Possible dates are wednesday, 8.30 am or wednesday, 4pm. Interested students may give their preferences (see contact above).
We start with the mapping degree for mappings between manifolds and connections to the de Rham cohomology. Afterwards, we discuss the Hopf invariant and its connections to the classical winding number of closed curves which again is based on the mapping degree. Starting from the Hopf map we will have a look at the foundation of so called principal bundles. We will then discuss selected problems and applications like magnetic monopoles, Belavin-Polyakov solitons and other harmonic maps, Ginzburg-Landau vortices, possibly foundations of Yang-Mills theory. Necessary tools from the calculus of variations will be explained.
Written or oral