Mathematisches Institut der Universität Bonn

S4B1 - Graduate Seminar in Analysis - KAM and Nash-Moser

Winter term 2024/25

Dr. Jan Bohr

Prof. Dr. Herbert Koch

Organisational details

• Time and place: Wed 10 (c.t) - 12, SR1.007, Endenicher Allee 60, first seminar: Wed 16th October

• First preliminary meeting: Wed 24.07.24, 16:15, SR0.011, Endenicher Allee 60


• [Update, 5 Aug] The seminar still has open spots and we encourage everyone who is interested to get in touch with us. Also new Masters students are welcome! There will be an additional brief planning meeting before the first talk.
  
  
• Second preliminary meeting: Wed 16.10.24, 10:15, SR0.011, Endenicher Allee 60


• If there are any questions, please get in touch with one of the organisers. If you are a participating Masters student, please register on Basis.0

  Basis page

  eCampus page

Overview

The inverse function theorem for Banach spaces is ubiquitous in nonlinear analysis and differential geometry. Its usage is however limited to situations where there is no loss of derivatives, that is, where one may choose function spaces of a fixed regularity in which the linearised problem can be solved. The Nash-Moser theorem is an inverse function theorem that can deal with a loss of derivatives and is commonly formulated on spaces of smooth functions (or more generally on Frechet spaces). In the seminar we will discuss and prove a version of the Nash-Moser theorem and explore some situations where its usage is/is not warranted. We'll also explore an application of the ideas behind the Nash-Moser theorem to Hamiltonian mechanics and discuss a version of the celebrated KAM (Kolmogorov-Arnold-Moser) theorem.

See here for more information, including a list of talks and literature recommendations.

Prerequisites: Basics of linear PDE and functional analysis

Schedule of talks