28. Internationales Internetseminar "Ergodic structure theory and applications"

The 28th Internet Seminar on Evolution Equations is entitled "Ergodic structure theory and applications". We aim to provide a robust and self-contained introduction to the following topics during the lecture phase, which will serve as a foundation for more specialized topics in the project phase:

• Introduction to measure-preserving systems, basic recurrence and convergence theorems; application: Weyl's equidistribution theorem.
• Compact and weakly mixing systems, Jacobs-de Leeuw–Glicksberg decomposition, classification of compact systems (Mackey theory, Pontryagin duality).
• Furstenberg's correspondence principle; applications: Furstenberg–Sárközy theorem, Roth's theorem.
• Furstenberg–Zimmer structure theory and multiple recurrence; applications: Szemerédi's theorem.
• Host–Kra structure theory with a focus on Conze–Lesigne systems; applications: the inverse theorem for the Gowers

We expect the participants to have a basic knowledge in functional analysis, bounded operators, foundations of Hilbert spaces and some familiarity with the Fourier transform and functions in one complex variable.

The concept of the “Internet Seminar” originates in 1998 when Rainer Nagel (Tübingen) organized the first Internet Seminar. Since then, many schools have been organized in the same spirit and the experience of the previous editions has shown that these schools are much more effective than traditional schools where participants have a much more passive role. The course is organised in three phases.

• In Phase 1 (October-February), a weekly lecture will be freely accessible over the internet via the ISEM website. The aim of the lectures is to present the theoretic background which lies behind current ongoing research.
• In Phase 2 (April - June), the participants will form small international groups to work on diverse projects which supplement the theory of Phase 1 and provide some applications of it.
• Finally, Phase 3 (June 2025) consists in a final workshop, where the teams will present their projects and additional lectures will be delivered by leading experts.

ISem team

Asgar Jamneshian (Dresden), Henrik Kreidler (Wuppertal), Rajula Srivastava (Bonn)

Website

https://sites.google.com/view/isem28/welcome