Special Lagrangians from the perspective of Morse theory

In this talk, we consider a Lagrange multipliers problem where the constraint is a section of a bundle $E \rightarrow M$. We relate the Morse homology of a function restricted to $s^{-1}(0)$ to the Morse homology of the associated Lagrange function on the total space $E^{*}$. We then discuss a similar (infinite- dimensional) Lagrange multipliers problem that first appeared in Donaldson and Segal’s paper Gauge Theory in Higher Dimensions II. The long term goal is to apply Floer theory to a functional whose critical points are generalizations of three-dimensional, special Lagrangian submanifolds. We describe the relevant functionals, critical points, and gradient trajectories.