Emily Windes, The University of Rochester

Title: Special Lagrangians from the perspective of Morse theory

Abstract: In this talk, we consider a Lagrange multipliers problem where the constraint is a section of a bundle E -> M. We relate the Morse homology of a function restricted to the zero set of the section to the Morse homology of the associated Lagrange function on the total space E*. Then we discuss a similar, infinite-dimensional Lagrange multipliers problem appearing 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 a generalization of three-dimensional, special Lagrangian submanifolds.