|Location:||MSRI: Simons Auditorium|
The recent proof Demailly's conjecture by Witt Niströrm gives another evidence that pluripotential theory play a key role when working with complex Monge-Ampère equations in order to solve problems in differential and algebraic geometry. In this talk we investigate pluripotential tools: we characterize the
Monge-Ampère energy class E in terms of "envelopes". And in order to do that, we develop the theory of weak geodesic rays in a big cohomogy class. We also give a positive answer to an open problem in pluripotential theory. This is a joint work with Tamas Darvas and Chinh Lu.