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# Analysis Seminar – Bingyuan Liu (University of California, Riverside) Geometry of the @-Neumann problem and the D{F index

## April 27 @ 3:00 pm - 4:00 pm

Abstract.

We shall rst introduce the classical works of Hormander and Kohn on the L2 estimates of the @(-Neumann) problem on bounded domains and then describe applications in complex geometry. It turns out that the boundary geometry plays the fundamental role in the Sobolev estimates of the @ solution. The Diederich{Fornss index is the geometric invariant which predicts the estimates. We shall try to reveal the mysterious relations between the boundary geometry, the index and the Sobolev estimates.