Homeomorphisms in symplectic topology and dynamics

ERC HSD (January 2020-December 2024)

The broad goal of the HSD project is to explore continuous symplectic topology and its interactions with symplectic topology and dynamical systems.

Here is a (somewhat outdated) brief introductory talk on C⁰ symplectic geometry and two of the most well-known problems in the field.

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This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 851701)

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News and upcoming events:

• Frontiers of quantitative symplectic and contact geometry at Mittag-Leffler, June 27-July 1, 2022.
• Conference : Giroux 60 — Convexity in contact and symplectic topology, July 4-8, 2022.

The Research Group:

PI: Sobhan Seyfaddini

Postdocs:

• Dusan Joksimovic
  January 2020-
  No symplectic-Lipschitz structures on S^2n≥4, arXiv:2106.04290
  
  
• Erman Cineli
  Sep 2021-
  

PhD students:

• Yusuke Kawamoto (external funding, co-supervision with C. Viterbo)
  Sep. 2018 - Aug. 2021
  Homogeneous quasimorphisms, C⁰-topology and Lagrangian intersection, arXiv:2006.07844
  Subsequent position: postdoc at Montreal 2021-2022, Weyl instructor ETH-Zürich 2022-2025.

Publications of the PI:

1. Quantitative Heegaard Floer cohomology and the Calabi invariant (with Dan Cristofaro-Gardiner, Vincent Humilière, Cheuk Yu Mak, and Ivan Smith). ArXiv 2105:11026. pdf
• Video.
2. Proof of the simplicity conjecture (with Dan Cristofaro-Gardiner and Vincent Humilière). ArXiv:2001.01792. pdf
• An article on our work.
• Video.
3. PFH spectral invariants on the two-sphere and the large scale geometry of Hofer's metric (with Dan Cristofaro-Gardiner and Vincent Humilière). To appear in J. Eur. Math. Soc. (JEMS).pdf
• Video.
4. The Anosov-Katok method and pseudo-rotations in symplectic dynamics (with Frédéric Le Roux). To appear in Journal of Fixed Point Theory and Applications, special issue in honour of Claude Viterbo. pdf
5. An Arnold-type principle for non-smooth objects (with Lev Buhovsky and Vincent Humilière). To appear in Journal of Fixed Point Theory and Applications, special issue in honour of Claude Viterbo. pdf

Events (co-)organized:

• Informal Smplectic Reading Group, Nov. 2021-
• Smplectix seminar, Jan. 2020-
• IHP Trimester on symplectic and contact geometry, April 19th - July 16th, 2021.
• IHP Conference Advances in symplectic topology, May 17-21, 2021.

Visitors:

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Timeline: