Föstudaginn 27. maí mun Eggert Karl Hafsteinnson kynna meistraprófsritgerð sína. Fyrirlesturinn byrjar klukkan 11:00 í V-152.
Leiðbeinandi: Benedikt Steinar Magnússon
Prófdómari: Tyson Ritter, Stafangri, Noregi
Titill: Random Polynomials & Convex Bodies
Ágrip: This thesis examines how three results in pluripotential theory can be generalized by replacing the usual polynomials with polynomials with respect to a convex body. The thesis introduces the concepts and results from pluripotential theory, then the various established generalizations, followed by their synthesis and, as its first result, a demonstration of a generalized link between Bergman kernels of a weighted polynomial space with respect to a convex body and pluricomplex Green functions. This result is then applied to reveal the asymptotic relation between a certain set of random polynomials and a pluricomplex Green function, which comprises the second result. Finally, the first result is again used to demonstrate how a certain set of random polynomials is related asymptotically to a pluricomplex Green function, similar to the second result, but from the perspective of the examination of the relationship in the weak sense of currents after a particular partial differential operator has been applied.