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Homeomorphisms in symplectic topology and dynamics

Project description

Advancing the field of continuous symplectic topology

Continuous symplectic topology studies continuous analogues of smooth symplectic objects, such as symplectic and Hamiltonian homeomorphisms, and investigates the persistence of various symplectic phenomena under uniform limits and perturbations. The EU-funded HSD project will explore continuous symplectic topology from two different perspectives. The first is a symplectic topological perspective that is informed by Gromov’s soft and hard symplectic geometry. The second one is motivated by the recent interactions of continuous symplectic topology and dynamical systems, which fall under the new field of symplectic dynamics.

Objective

The subject of this proposal is the field of continuous symplectic topology. This is an area of symplectic topology which defines and studies continuous analogues of smooth symplectic objects such as symplectic and Hamiltonian homeomorphisms and asks questions about persistence of various symplectic phenomena under uniform limits and perturbations.

Our aim is to explore, and further develop, continuous symplectic topology from two different perspectives: The first is a symplectic topological perspective which is informed by Gromov’s soft and hard view of symplectic topology. The second is motivated by the recent interactions of continuous symplectic topology and dynamical systems and it falls under the new field of symplectic dynamics.

We outline an extensive research program in line with the above two viewpoints. On the one hand, we propose to develop new tools for the advancement of the field via the medium of barcodes which will serve as a replacement of Floer homology for homeomorphisms. On the other hand, we propose new approaches towards several important questions in the field including the symplectic four-sphere problem which asks if non-symplectic manifolds, such as the four-sphere, could admit the structure of a topological symplectic manifold, and the simplicity conjecture which asks if the group of compactly supported area-preserving homeomorphisms of the disc is a simple group.

Fields of science (EuroSciVoc)

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Keywords

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Programme(s)

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Topic(s)

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Funding Scheme

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ERC-STG - Starting Grant

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Call for proposal

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(opens in new window) ERC-2019-STG

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Host institution

EIDGENOESSISCHE TECHNISCHE HOCHSCHULE ZUERICH
Net EU contribution

Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.

€ 328 770,20
Address
Raemistrasse 101
8092 Zuerich
Switzerland

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Region
Schweiz/Suisse/Svizzera Zürich Zürich
Activity type
Higher or Secondary Education Establishments
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Total cost

The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.

€ 328 770,20

Beneficiaries (2)

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