Floer Theories in Symplectic Topology and Gauge Theory

I will sketch the basic idea of floer theory, in particular its symplectic version for pairs of Lagrangians and its instanton version for homology 3-spheres.

In a joint project with Dietmar Salamon we define a new Flkoer theory for 3-manifolds with boundary, using the instanton equation with Lagrangian boundary conditions (containing nonlocal conditions on the holonomy).

The underlying PDE exhibits some unexpected semi-global behaviour. This can be understood as evidence that the new Floer homology is an intermediate object between the instanton Floer homology and the symplectic Floer homology and can thus be used to prove a conjecture of Atiyah and Floer relating these.

Refreshments will be served at 3:45 p.m. in the Faculty Lounge, Math Annex (Room 1115).