September 2016 – LECTURE CANCELLED
TITLE: Pluripotential theory on calibrated manifolds
ABSTRACT: A calibrated manifold carries a geometry of distinguished -submanifolds and -currents. This is relatively well-known. However, also carries distinguished analytic objects: the -plurisubharmonic functions, which are, in a sense, dual to the currents. Somewhat surprisingly much of the classical pluripotential theory in several complex variables extends to the context of calibrations. This includes -operators, notions of convexity, maximal functions (the analogues of solutions to the complex Monge-Ampère equation), and solving the Dirichlet Problem for such functions. I will discuss what is known in this area, and pose a number of questions and problems.