Frauenfelder, Urs Adrian:Post Doctorial Fellow,Geometry

Arnold-Givental conjecture, Hamiltonian group actions, Floer homology, Symplectic vortex equations
Research Interest:
Symplectic geometry
Research Activities:
For some class of Lagrangian submanifolds in Marsden-Weinstein quotients which are fixed point sets of an antisymplectic involution I proved the Arnold-Givental conjecture. This conjecture asks for a lower bound in terms of the homology of the Lagrangian on the number of intersection points of the Lagrangian which its image under a Hamiltonian isotopy if the image intersects the Lagrangian transversally. The proof makes use of moment Floer homology. The boundary operator in moment Floer homology is defined by counting solutions of the symplectic vortex equations whose moduli spaces have better compactness properties then the original Floer equations.