题目： Lectures on Polynomial and Rational Convexity: Introduction, basic properties and some applictions

报告人：Prof. Nikolay Shcherbina

(Bergische Universit¨at Wuppertal GERMANY)

Abstract :

Lectures 1-2: Polynomial and Rational approximation in C. Theorems of Runge and Mergelyan. Definition and some basic properties of polynomially and rationally convex sets in Cⁿ. Theorem of Oka-Weil.

Lectures 3-4: Definition and main properties of plurisubharmonic functions. Oka’s characterization of polynomially convex sets. Characterization of polynomially convex sets using globally defined plurisubharmonic functions. Rossi’s local maximum principle.

Lectures 5-6: Equivalence of different characterizations of polynomial convexity. Cohomological properties of polynomially convex sets. Proof of the Browder’s theorem using plurisubharmonic functions. Solution of the Dirichlet Problem for Levi flat graphs.

Lectures 7-8: Applications of polynomial convexity to the study of

Kobayashi and Bergman metrics of Model domains and to the solution

of the Nishino problem on the structure of pluripolar graphs.

时间：3月8、15、22、25日下午14:00

地点：565net必赢客户端教二楼713教室

联系人：张利友

欢迎全体师生积极参加！