Several Complex Variables SeminarFall 2018 - Spring 2019
Time: Wednesday, 16:30 - 17:30
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TIME | SPEAKER | TITLE |
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.