Organisers: Sebastián Daza-Kühn, João Nuno Mestre, Lennart Obster
Time: Fridays 14:30 - 16:30
Time: Thursdays 14:30-16:30
Room: 5.5 (DMUC)
The weekly learning seminar is to 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. There will be an emphasis on learning the basics on (tame) Fréchet spaces and (tame) Fréchet manifolds (and in the paper there are many examples). If time permits, we will discuss some applications (which will depend on the audience).
Useful complementary references are:
Roy Wang, "The Nash-Moser theorem and applications." Master Thesis, Utrecht University, 2012
Morris W. Hirsch, "Differential Topology", Springer GTM volume 33, 1976
24-10-2024 - Week 1: Introduction and planning; start with I1 Fréchet spaces. - Lennart Obster
31-10-2024 - Week 2: l1 Fréchet spaces. - Sebastián Daza-Kühn
14-11-2024 - Week 3: Spaces of sections of vector bundles - Lennart Obster
21-11-2024 - Week 4: Jets - Sebastián Daza-Kühn
28-11-2024 - Week 5: Weak and strong topologies - Sebastián Daza-Kühn
05-12-2024 - Week 6: More examples; Properties of Banach spaces - Lennart Obster
12-12-2024 - Week 7: Hahn-Banach, Baire Category theorem, Open mapping theorem - Lennart Obster
16-01-2025 - Week 8: Inverse Function Theorem in the Banach setting - Alexander Kovačec
23-01-2025 - Week 9: Integral and differential calculus on Fréchet spaces - Alexander Kovačec
30-01-2025 - Week 10: Integral and differential calculus on Fréchet spaces, Part 2 - Alexander Kovačec
14-02-2025 - Week 11: Concluding the proof of the Inverse Function Theorem for Banach spaces - Alexander Kovačec
21-02-2025 - Week 12: Manifolds and vector bundles - João Nuno Mestre
07-03-2025 - Week 13: Directional derivative, properties, and the chain rule - Sebastián Daza-Kühn
14-03-2025 - Week 14: Higher derivatives - Sebastián Daza-Kühn
04-04-2025 - Week 15: Minimal surfaces - Alexander Kovačec
11-04-2025 - Week 16: Fréchet manifolds; the example of spaces of sections of a submersion - Lennart Obster
16-04-2025 - Week 17: Fréchet manifolds: more examples - Lennart Obster
22-04-2025 - Week 18: Vector bundles over Fréchet manifolds - Sebastián Daza-Kühn
07-05-2025 - Week 19: Maps of manifolds - Sebastián Daza-Kühn
16-05-2025 - Week 20: Connections and Lie groups - Lennart Obster