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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.

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

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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The information about "TRANSHOLOMORPHIC" are provided by the European Opendata Portal: CORDIS opendata.

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