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TRANSHOLOMORPHIC SIGNED

New transversality techniques in holomorphic curve theories

Total Cost €

0

EC-Contrib. €

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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.

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

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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