Séminaire Géométrie et applications
organisé par l'équipe Géométrie
-
Nikolas Adaloglou
Which symplectic forms on S2xS2 have Lagrangian Klein bottles?
3 novembre 2025 - 14:00Salle de séminaires IRMA
Using (almost) toric fibrations and their visible Lagrangians we can construct many novel and interesting examples of Lagrangian submanifolds of symplectic 4 manifolds. Naturally, one can ask whether visible Lagrangians are all the Lagrangians that exist, or, in other words, how faithful the pictures coming from almost toric fibrations are. I will answer this question for Klein bottles in (S2xS2,ω_λ), i.e. the product of two spheres where the first factor has area 1 and the other factor has area λ. In particular, I will first construct a visible Lagrangian Klein bottle when λ<2. Then I will show that no Lagrangian Klein bottles exist otherwise. The key input for obstructing the existence of the Klein bottles is Luttinger surgery along with techniques of (compact) pseudoholomorpic curves and Seiberg-Witten theory. This is joint work with J. Evans. -
Amanda Hirschi
TBA
10 novembre 2025 - 14:00Salle de séminaires IRMA
TBA -
Amanda Hirschi
TBA
10 novembre 2025 - 14:00Salle de séminaires IRMA
TBA -
Francesco Morabito
Braids and Morse/Floer complexes
17 novembre 2025 - 14:00Salle de séminaires IRMA
In this talk we focus our attention on compactly supported Hamiltonian diffeomorphisms of the plane. To each pair of distinct fixed points we can associate an integer, the linking number of the pair. Moreover, we can describe the dynamics of the diffeomorphism itself via the Morse complex of a generating function. This Morse complex is classically known to be filtered by action. In this talk we are going to show how we can equip its tensor power with a secondary filtration which keeps track of the linking numbers of pairs of orbits. The proof relies on foundational work on twist maps carried out by Patrice Le Calvez in the '90s, and on uniqueness properties of generating functions. Moreover, we are going to explain how using this language one may provide a finite-dimensional proof of Hofer-lower semicontinuity of the topological entropy, first proved by Alves and Meiwes. One can define a similar filtration on Floer complexes using intersection products of pseudo-holomorphic cylinders as defined by Siefring: if time permits, we are going to provide a sketch of this construction. -
Shah Faisal
TBA
24 novembre 2025 - 14:00Salle de séminaires IRMA
TBA -
Giles Gardam
TBA
1 décembre 2025 - 14:00Salle de séminaires IRMA
TBA -
Santharoubane Ramanujan
TBA
8 décembre 2025 - 14:00Salle de séminaires IRMA
TBA -
Baptiste Séraille
à préciser
8 décembre 2025 - 15:30Salle de séminaires IRMA
-
Neige Paulet
TBA
15 décembre 2025 - 14:00Salle de séminaires IRMA
TBA -
Sergi Burniol-Clotet
TBA
12 janvier 2026 - 14:00Salle de séminaires IRMA
TBA -
Lamine Messaci
TBA
26 janvier 2026 - 14:00Salle de séminaires IRMA
TBA