Description
The principal actors of complex analysis and geometry are holomorphic functions. Nonetheless, in the course of the 20th century another type of functions, called plurisubharmonic, rose to a most prominent supporting role. These functions are complex analogs (and at the same time, generalizations) of convex functions. They are relevant, because in many situations properties of plurisubharmonic functions have direct implications on properties of holomorphic functions.
Berndtsson's theorem, on a basic level, says that certain operations involving holomorphic and plurisubharmonic functions produce plurisubharmonic functions. After introducing the necessary notions, in this talk I will formulate an instance of the theorem, and discuss an application.