Course «Several Complex Variables: Outline»

St. Petersburg State University and Euler International Mathematical Institute are happy to announce a new minicourse, headed by prof. Norman Levenberg. Lectures scheduled to Tuesdays and Thursdays starting 28 September, 6 pm (Moscow time). To attend the lectures, please join zoom channel 862-736-624-77. If you do not know the password, please write an email to Yurii Belov. Video records of the course are available here.

 

Course description

We propose approximately 10 lectures over a period of 5 weeks with one lecture each Tuesday and Thursday beginning at 6 PM Moscow time. The duration of each lecture should be approximately 100 minutes – two 50 minute sessions with a ten-minute break in between. The proposed starting date of the course is Tuesday, September 28 which would mean lectures Sept. 28 and 30; Oct. 5, 7, 12, 14, 19, 21, 26 and 28 but we are very flexible.

Program:

  • Introduction. Revisiting C: Cauchy-Pompieu formula, Runge’s theorem, and solving ̄∂; onto Cd and holomorphic functions, Cauchy integral formula for polydisks, power series, solving ̄∂ with compact support, Hartogs’ Kugelsatz;
  • Domains of holomorphy and holomorphic convexity. Definition and examples of domain of holomorphy, holomorphic convexity, Cartan-Thullen theorem;
  • Integral formulas and pseudoconvexity. Bochner-Martinelli kernel, Cauchy-Fantappie forms, Cauchy-Szegoe kernel, polynomial convexity and Oka-Weil theorem, plurisubharmonic functions and pseudoconvexity (4) L2 − ̄∂ techniques. Hoermander’s L2 − ̄∂ theory and a solution of the Levi problem;
  • Cousin I and II problems. Cousin problems and applications to approximation theory;
  • (*if time) Introduction to pluripotential theory. Extremal plurisubharmonic functions and the complex Monge-Ampere operator.

Everyone is welcome!