Symplectic Dynamics in Aachen

RWTH Aachen, Germany

The goal of this meeting is to gather experts in symplectic dynamics, aiming to discuss problems and methods at the frontier of the research in the field. Pseudo-holomorphic curves, Floer theory, methods from the Calculus of Variations for the action functional, like Clarke's duality, topological constructions with pseudo-holomorphic curves in low-dimensions, like Fried's surgery, are among the main topics. There will be plenty of free time for discussions, and of opportunities to socialize.

Date

September 16-20, 2024

Speakers:

• Marcelo Atallah

• Gabriele Benedetti

• Vincent Colin

• Laurent Côté

• Oliver Edtmair

• Urs Frauenfelder

• Helmut Hofer (TBC)

• Vincent Humilière

• Leonardo Macarini

• Marco Mazzucchelli 

• Yaron Ostrover

• Margherita Sandon

• Pedro Salomão

Minicourses:

• Jungsoo Kang, "Clarke duality and applications": In contrast to the Hamiltonian action functional, Clarke’s dual action functional is defined only for convex Hamiltonian functions. However, it has better analytical properties. For example, the Morse homology of Clarke’s dual functional is well defined, and minimal periodic orbits arise as minimizers. In this mini-course, I will discuss such properties of Clarke’s dual functional, an isomorphism between the Morse homology of the dual functional and the Floer homology of the Hamiltonian functional, and some applications based on this isomorphism.

• Vinicius Ramos, "Billiards and Symplectic Topology": In this mini-course, we will talk about billiard dynamics and the surprising link between the Mahler and the Viterbo conjectures. We will then explain how the integrability of many billiards can be used to prove that many domains in cotangent bundles are toric and how to use this to find very interesting sharp symplectic embeddings.

Organizing Commitee:

Alberto Abbondandolo (Ruhr Universität Bochum)

Luca Asselle (Ruhr Universität Bochum)

Umberto Hryniewicz (RWTH Aachen)

Participation is open. If you wish to participate, please inform us by sending an e-mail to sekretariat@mathga.rwth-aachen.de