Lagrangian boundary conditions for anti-self-dual instantons and the   Atiyah-Floer conjecture
  The purpose of this survey is to explain an approach to the Atiyah-Floer conjecture via a new instanton Floer homology with Lagrangian boundary conditions. This is a joint project with Dietmar Salamon. This paper also provides a rough guide to the analysis of anti-self-dual instantons with Lagrangian boundary conditions (in earlier papers), which is the crucial ingredient of our approach. 
Katrin Wehrheim