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

Winter term 2024/25

Dr. Jan Bohr
Prof. Dr. Herbert Koch

Organisational details

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 in 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 then 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

October 9- Talk 01 TBA

October 16- Talk 02 TBA

October 23- Talk 03 TBA

October 30- Talk 04 TBA

November 6- Talk 05 TBA

November 13- Talk 06 TBA

November 20- Talk 07 TBA

November 27- Talk 08 TBA

December 4- Dies Academicus

December 11- Talk 09 TBA

December 18- Talk 10 TBA

December 18- Talk 11 TBA

December 25- Christmas break

January 1- Christmas break

January 8- Talk 12 TBA

January 15- Talk 13 TBA

January 22- Talk 14 TBA