KTH/SU Mathematics Colloquium
08-02-27
Tobias Ekholm, Uppsala University
Holomorphic curves and Morse type inequalities
for exact Lagrangian immersions
A series of conjectures in symplectic geometry (formulated by Arnold)
generalizes the Morse inequalities from finite dimensional topology to
problems in symplectic and contact geometry. In groundbreaking works
from the 1980's Gromov and Floer used holomorphic curves to establish
some of these conjectures. In the talk we discuss how to apply
holomorphic curve techniques to demonstrate important special cases of
the following (still open) conjecture: the number of double points of
any exact Lagrangian submanifold of complex n-space is at least as
large as half the rank of its total homology.