Spiro Karigiannis, Pure Mathematics, University of Waterloo
"Intro to Calibrations, Instantons, and Branes"
I will introduce the concept of a calibration on a Riemannian manifold and its associated calibrated submanifolds. These are special minimal submanifolds defined by a system of first order, often fully nonlinear, partial differential equations. Following a proof of the fundamental theorem of calibrated geometry, and a brief discussion of examples, I will present the approach of Leung-Lee in the language of instantons and branes on manifolds with vector cross product.