### Monday September 12, 2005, 4:00 PM

### tea at
3:30 PM at the Math Department lounge (Goldsmith 300)

**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.