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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.

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

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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