Several Complex Variables Seminar

Fall 2018 - Spring 2019

Time: Wednesday, 16:30 - 17:30
Location: MA 105

Schedule of talks:


September 19 Liz Vivas (OSU) Non-autonomous 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) Multi-Cauchy transform and the d-bar 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 multi-Cauchy transform on product spaces with 1-dim factors. Then we will show how to use this transform to construct a solution of the d-bar 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.