Several Complex Variables SeminarFall 2018  Spring 2019
Time: Wednesday, 16:30  17:30


TIME  SPEAKER  TITLE 
September 19  Liz Vivas (OSU)  Nonautonomous holomorphic bifurcation 
September 26  Jeff McNeal (OSU)  Irregularity of the Bergman projection, breakdown of function theory 
October 17  Jue Xiong (OSU)  Norm convergence of partial sums of H^1 functions 
October 24  Liwei Chen (OSU)  MultiCauchy transform and the dbar equation on product spaces 
October 31  
November 14  
November 28  
December 12  
January 9 
September 19: I'd explain what's the role of bifurcation on complex dynamics in one complex variable, the generalization to two variables and give an application.
September 26: I'll discuss examples of domains where its been recently discovered that the Bergman projection does not map L^p to itself. Consequences will also be discussed.
October 17: A classical observation of Riesz says that truncations of a general \sum_{n=0}^{\infty}a_nz^n in the Hardy space H^1 do not converge in H^1. A substitute positive result is proved: these partial sums always converge in the Bergman norm A^1. The result is extended to complete Reinhardt domains in C^n. A new proof of the failure of H^1 convergence is also given.
October 24: In this talk, we will introduce the multiCauchy transform on product spaces with 1dim factors. Then we will show how to use this transform to construct a solution of the dbar equation. In the same time, we will study the L^p regularity of this solution operator. If time allows, we will extend this idea to general product spaces with higher dimensional factors.