Symplectic capacities of domains close to the ball and quasi-invariant contact forms | Vidéo | Carmin.tv

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Symplectic capacities of domains close to the ball and quasi-invariant contact forms

By Alberto Abbondandolo

Appears in collection : From smooth to $C^{0}$ symplectic geometry: topological aspects and dynamical implications / Géométrie symplectique de lisse à $C^{0}$: aspects topologiques et implications dynamiques

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.

Information about the video

Date of recording 06/07/2023
Date of publication 21/07/2023
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Jean Petit
Format MP4

Citation data

DOI 10.24350/CIRM.V.20068203
Cite this video Abbondandolo, Alberto (06/07/2023). Symplectic capacities of domains close to the ball and quasi-invariant contact forms. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20068203
URL https://dx.doi.org/10.24350/CIRM.V.20068203

Domain(s)

Symplectic Geometry

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

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