## Benedikt Steinar Magnússon (12/02/16)

Sigurður Örn Stefánsson, febrúar 11, 2016

Math Colloquium

### Speaker: Benedikt Steinar Magnússon Title: Pluripotential theory in several complex variables explained by the Dirichlet problem in the plane

Location: V-157, VRII.
Time: Friday, February 12 at 13:20.

### Abstract:

The goal is to give a brief introduction to pluripotential theory in several complex variables using the Dirichlet problem in the plane as a starting point. We will start by looking at different solution methods for the Dirichlet problem. One of them, the Perron method, motivates our approach to similar problems in several complex variables. But when we look at the ingredients of the Dirichlet problem it turns out that not all of them generalize well to several complex variables so we will have to carefully choose what we bring with us on our adventure into $$\mathbb C^n$$.

The problems in several complex variables we consider includes for example the global extremal function which is not only useful in pluripotential theory but also in holomorphic function theory.