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Symplectic capacities of domains close to the ball and quasi-invariant contact forms
Multi angle
Authors : Abbondandolo, Alberto (Author of the conference)
CIRM (Publisher )
53D35 - Global theory of symplectic and contact manifolds
57R40 - Embeddings
37J11 - Symplectic and canonical mappings
CIRM (Publisher )
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Abstract :
An old open question in symplectic dynamics asks whether all normalized symplectic capacities coincide on convex domains. I will discuss this question and show that the answer is positive if we restrict the attention to domains which are close enough to a ball. The proof is based on a “quasi-invariant” normal form in Reeb dynamics, which has also implications about geodesics in the space of contact forms equipped with a Banach-Mazur pseudo-metric. This talk is based on a joined work with Gabriele Benedetti and Oliver Edtmair.
Keywords : symplectic capacities; Viterbo's conjecture
MSC Codes : Keywords : symplectic capacities; Viterbo's conjecture
53D35 - Global theory of symplectic and contact manifolds
57R40 - Embeddings
37J11 - Symplectic and canonical mappings
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Information on the Video
Film maker : Petit, JeanLanguage : English Available date : 21/07/2023 Conference Date : 06/07/2023 Subseries : Research talks arXiv category : Symplectic Geometry Mathematical Area(s) : Geometry ; Topology Format : MP4 (.mp4) - HD Video Time : 01:04:33 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-07-06_Abbondandolo_1.mp4 
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Information on the Event
Event Title : From smooth to $C^{0}$ symplectic geometry: topological aspects and dynamical implications / Géométrie symplectique de lisse à $C^{0}$: aspects topologiques et implications dynamiquesEvent Organizers : Benedetti, Gabriele ; Humilière, Vincent ; Leclercq, Rémi ; Sandon, Sheila ; Seyfaddini, Sobhan Dates : 03/07/2023 - 07/07/2023 Event Year : 2023 Event URL : https://conferences.cirm-math.fr/2759.html
Citation Data
DOI : 10.24350/CIRM.V.20068203Cite this video as: Abbondandolo, Alberto (2023). Symplectic capacities of domains close to the ball and quasi-invariant contact forms. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20068203 URI : http://dx.doi.org/10.24350/CIRM.V.20068203 |
See Also
- [Multi angle] The Humilière completion and some applications / Author of the conference Viterbo, Claude.
- [Multi angle] Contact topology and thermodynamics / Author of the conference Polterovich, Leonid.
- [Multi angle] Symplectic mapping class groups: structural properties from smooth to $C^{0}$ / Author of the conference Keating, Ailsa.
- [Multi angle] The spectral norm, rigidity and all that / Author of the conference Gurel, Basak.
Bibliography
- Abbondandolo, Alberto, and Gabriele Benedetti. "On the local systolic optimality of Zoll contact forms." Geometric and Functional Analysis 33.2 (2023): 299-363. - http://dx.doi.org/10.1007/s00039-023-00624-z
- Abbondandolo, Alberto, and Gabriele Benedetti. "Symplectic capacities of domains close to the ball and quasi-invariant contact forms". (in preparation) -
- Edtmair, Oliver. "Disk-like surfaces of section and symplectic capacities." arXiv preprint arXiv:2206.07847 (2022). - https://doi.org/10.48550/arXiv.2206.07847
