There will be a learning seminar on the inverse function theorem of Nash and Moser starting this semester at the Department of Mathematics:
In this weekly learning seminar we will study Hamilton's paper:
Richard S. Hamilton. "The inverse function theorem of Nash and Moser." Bulletin (New Series) of the American Mathematical Society, 7(1), 65-222, July 1982.
The goal is to understand, in detail, the inverse function theorem of Nash and Moser. We will follow the paper by Hamilton. Therefore, there will be an emphasis on learning the basics on (tame) Fréchet spaces and (tame) Fréchet manifolds. If time permits, we will discuss some applications (which will depend on the audience).
Here you can find some brief explanation of the context:
https://en.wikipedia.org/wiki/Nash%E2%80%93Moser_theorem https://en.wikipedia.org/wiki/Nash%E2%80%93Moser_theorem#Hamilton's_formulation_of_the_theorem Organisers: Sebastián Daza-Kühn, João Nuno Mestre, Lennart Obster
Schedule
- Lennart Obster (CMUC), Introduction to Fréchet spaces, 24-10-24.- Sebastián Daza (CMUC), Introduction to vector bundles, 31-10-24.- Lennart Obster (CMUC), Spaces of sections of vector bundles as Frechét spaces, 14-11-2024.- Sebastián Daza (CMUC), Jet bundles, 21-11-2024.- Sebastián Daza (CMUC), Weak and strong topologies in terms of jet bundles, 28-11-2024.- Lennart Obster (CMUC), Examples of Frechét spaces and properties of Banach spaces, 05-12-2024.- Lennart Obster (CMUC), The Hahn-Banach theorem, Baire category theorem, and open mapping theorem in the Frechét setting, 12-12-2024.
