Speaker: Edward Goldstein
Title: Minimal submanifolds and calibrations
Abstract: We'll begin by discussing the second fundamental form of submanifolds in Riemannian manifolds, first variation of volume and minimal submanifolds. We'll exhibit some examples of minimal submanifolds (fixed point sets of isometries, calibrated submanifolds) and present a volume comparison theorem for minimal submanifolds. Next we'll move onto pseudoholomorphic curves in symplectic manifolds and sketch a proof of Gromov's non-squeezing theorem.