CORDIS Project
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This project aims to advance the understanding of symplectic topology through new transversality techniques applied to pseudoholomorphic curves. It seeks to resolve key problems in the field, including the behavior of holomorphic curves and their implications for symplectic field theory and contact geometry.
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-Riema…
HUMBOLDT-UNIVERSITAET ZU BERLIN
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