Séminaire Géométrie et applications
organisé par l'équipe Géométrie
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Amanda Hirschi
On the Donaldson 4-6 question
10 novembre 2025 - 14:00Salle de séminaires IRMA
Two simply-connected smooth 4-manifolds are homeomorphic if and only if their products with S^2, are diffeomorphic. The Donaldson 4-6 question concerns an analogue of this fact in the symplectic category. Concretely, it asks whether the underlying smooth manifolds of two symplectic manifolds are diffeomorphic if and only if their products with S^2, equipped with the standard area form, are deformation equivalent. I will describe one example of a smooth 4-manifold admitting two symplectic forms which remain deformation inequivalent after taking the product with S^2, giving counterexamples to one implication of the conjecture. On the other hand, I will explain why two simply-connected symplectic manifolds, whose products with the sphere are deformation equivalent, have the same Gromov-Witten invariants. This is joint work with Luya Wang. -
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
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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 -
Timothé Lemistre
TBA
23 février 2026 - 14:00Salle de séminaires IRMA
TBA -
Manuel Rivera
TBA
9 mars 2026 - 14:00Salle de séminaires IRMA