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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.

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

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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