event
Mercredi 4 décembre 2024
Mercredi 4 décembre 2024
place
Salle de séminaires IRMA
Salle de séminaires IRMA
La journée portera sur différents thèmes de topologie et dynamique symplectique.
La rencontre est organisée dans le cadre du séminaire en ligne 4/10.
Organisateurs: Russell Avdek (Jussieu), Colin Fourel (IRMA), Amanda Hirschi (Jussieu), Anna Marduel (IRMA), Robin Riegel (IRMA), Yuan Yao (Nantes)
Orateurs:
- Yuan Yao (Nantes)
- Dylan Cant (Orsay)
Venue : Salle de séminaires de l'IRMA
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Mercredi 4 décembre 2024
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13:30
Yuan Yao, Nantes
A tourist’s introduction to the Conley Conjecture
In many fields of symplectic geometry, the geometric problem you care about is quickly/very easily reduced to properties of holomorphic curves, and most of the work is in either finding or studying holomorphic curves directly. However, in my limited experience, symplectic dynamics is not built like that. Often it is several ad-hoc, non-obvious constructions put together in an ingenious way that produces their results. This talk is a synopsis of my recent attempts to understand the subject. I will explain the proof of the Conley conjecture; except I will not give any proofs. I will instead focus on describing various structures and constructions in Hamiltonian Floer homology, and try to explain how these structures can be put together to give us extremely strong dynamics results like the Conley conjecture. -
15:00
Coffee Break
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15:30
Dylan Cant, Orsay
Shelukhin's proof of the Hofer-Zehnder conjecture
I will present Shelukhin's proof of the Hofer-Zehnder conjecture for closed symplectic manifolds with semi-simple quantum homology. His proof is based on estimating the number of finite bars in the Floer cohomology barcode for iterates of a Hamiltonian diffeomorphism, and uses the Z/pZ equivariant pants product and ideas from Smith theory. -
17:00
Discussion Session