Pluripotential theory

t_maths.potentialfig2


A potential associated to a distribution of electric charge on a body is a function whose gradient measures the electric field of the charge distribution in space.  Left to themselves, the electrons making up the charge will spread themselves over the body to minimize repulsive forces between them.  The resulting charge distribution is called the equilibrium measure, and its corresponding potential is called the equilibrium potential.  These notions are well-studied in complex potential theory, where 'space' is the complex plane.

In this research, we replace the complex plane by more general spaces, in particular, algebraic varieties, which are geometric sets given by solutions to polynomial equations.  There are analogues of the equilibrium measure and potential.  We are interested in questions such as:  How does complex potential theory generalize to this setting? And, how do geometric and algebraic properties of a variety affect its potential theory?

Researchers at the University of Auckland

Sione Ma`u