Advanced Topics in Analysis (University of Zurich)

Objective

Understanding of advanced techniques in analysis that are necessary for the understanding of modern pde theory, mathematical physics and geometric analysis.

Content

The lecture covers advanced topics in analysis that are essential for the understanding of several areas of modern analysis as e.g. the study of partial differential equations, mathematical physics and geometric analysis. Topics to be covered are: Fourier transform, distributions (generalized functions), weak derivatives, Sobolev spaces, weak and strong convergence, Sobolev inequalities, Schrödinger equation and existence of solutions via the direct method in the calculus of variations, properties of solutions of the Schrödinger equation. The lecture can be booked by B.Sc. students and runs for eight weeks, that is, it ends after the first half of the semester. Afterwards, it continues as a Bachelor/Master course in the second half of the semester under the title "Variational Methods in Analysis". The second part of the lecture is based on the first half. It aim at introducing the audience to techniques from the calculus of variations. Although these techniques are very general, we will, for the sake of concreteness, introduce them in the framework of certain models originating from atomic physics. More details can be found in the description of the lecture "Variational Methods in Analysis".

Resources