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TRANSHOLOMORPHIC SIGNED

New transversality techniques in holomorphic curve theories

Total Cost €

0

EC-Contrib. €

0

Partnership

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 TRANSHOLOMORPHIC project word cloud

Explore the words cloud of the TRANSHOLOMORPHIC project. It provides you a very rough idea of what is the project "TRANSHOLOMORPHIC" about.

planar    hutchings    conflict    reeb    whenever    setting    bifurcation    pseudoholomorphic    cobordisms    genericity    symplectic    techniques    involve    implications    nearby    symmetry    analogues    cotangent    analogous    embedding    cauchy    questions    folds    yau    dynamical    transversality    abstract    proving    causes    moduli    gopakumar    formula    full    geometry    progress    1985    foundations    topology    curves    instance    gromov    drawback    multiply    integrality    riemann    curvature    lagrangian    solutions    ech    dimension    negative    singular    examples    contact    calabi    refinements    spaces    orbits    analytical    played    curve    fundamental    structures    conjecture    completing    riemannian    perturbations    tackling    dimensional    neighboring    nonpositive    quasiflexible    vafa    dynamics    witten    overriding    covered    explored    holomorphic    bundles    invariants    proof    rigidity    manifolds    theory    super    homology    decisive    equation    wrong    relations    unravel   

Project "TRANSHOLOMORPHIC" data sheet

The following table provides information about the project.

Coordinator
HUMBOLDT-UNIVERSITAET ZU BERLIN 

Organization address
address: UNTER DEN LINDEN 6
city: BERLIN
postcode: 10117
website: www.hu-berlin.de

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Germany [DE]
 Total cost 1˙624˙500 €
 EC max contribution 1˙624˙500 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2017-COG
 Funding Scheme ERC-COG
 Starting year 2018
 Duration (year-month-day) from 2018-09-01   to  2023-08-31

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    HUMBOLDT-UNIVERSITAET ZU BERLIN DE (BERLIN) coordinator 1˙624˙500.00

Map

 Project objective

'In the study of symplectic and contact manifolds, a decisive role has been played by the theory of pseudoholomorphic curves, introduced by Gromov in 1985. One major drawback of this theory is the fundamental conflict between 'genericity' and 'symmetry', which for instance causes moduli spaces of holomorphic curves to be singular or have the wrong dimension whenever multiply covered curves are present. Most traditional solutions to this problem involve abstract perturbations of the Cauchy-Riemann equation, but recently there has been progress in tackling the transversality problem more directly, leading in particular to a proof of the 'super-rigidity' conjecture on symplectic Calabi-Yau 6-manifolds. The overriding goal of the proposed project is to unravel the full implications of these new transversality techniques for problems in symplectic topology and neighboring fields. Examples of applications to be explored include: (1) Understanding the symplectic field theory of unit cotangent bundles for manifolds with negative or nonpositive curvature, with applications to the nearby Lagrangian conjecture and dynamical questions in Riemannian geometry; (2) Developing a comprehensive bifurcation theory for Reeb orbits and holomorphic curves in symplectic cobordisms, leading e.g. to a proof that planar contact structures are 'quasiflexible'; (3) Completing the analytical foundations of Hutchings's embedded contact homology (ECH), a 3-dimensional holomorphic curve theory with important applications to dynamics and symplectic embedding problems; (4) Developing new refinements of the Gromov-Witten invariants based on super-rigidity and bifurcation theory; (5) Defining higher-dimensional analogues of ECH; (6) Proving integrality relations in the setting of 6-dimensional symplectic cobordisms, analogous to the Gopakumar-Vafa formula for Calabi-Yau 3-folds.'

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