The symplectic vortex equations and applications
Antragsteller:
Kai Cieliebak
Finanzierung: Deutsche
Forschungsgemeinschaft (DFG)
Programm: Schwerpunktprogramm Globale Differentialgeometrie
Laufzeit: 2003-2009
Mitarbeiter:
Jan Wehrheim
Oliver Fabert
Urs Frauenfelder
Martin Schwingenheuer
Janko Latschev
Alexander Stadelmaier
Fabian Ziltener
Andreas Gerstenberger
Zusammenfassung:
The symplectic vortex equations are equations on a symplectic
manifold with a Hamiltonian group action recently introduced
by Cieliebak, Gaio, Mundet and Salamon. Over the past years we
developed the solution theory of these equations. In this
project we will apply the symplectic vortex equations to questions in
global differential geometry.
The main application is to enumerative geometry, extending work of
Kontsevich-Manin on Gromov-Witten invariants and Givental on mirror
symmetry. Other applications concern Witten's conjecture on the
Verlinde algebra, and the relation between different gauge theoretical
invariants of smooth four-manifolds.