Anthony McCormick, Department of Pure Mathematics, University of Waterloo
“Calibrations”
We will discuss minimal submanifolds and show that the condition of being minimal amounts to the existence of a solution to a certain second order non-linear PDE. This will provide some motivation for defining calibrated submanifolds, as they are automatically minimal and their existence depends on solving a first order PDE as opposed to a second order one. In conclusion, we will discuss how the real and imaginary parts of the complex volume form on a Calabi-Yau manifold are calibrations before defining Special Lagrangian submanifolds and stating a simplified version of the SYZ conjecture.
M3 4001