##### Department of Mathematics,

University of California San Diego

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### Analysis Colloquium

## John D'Angelo

#### University of Illinois at Urbana - Champaign

## Positivity conditions in complex geometry

##### Abstract:

I will begin with some elementary remarks about Hermitian symmetric functions on complex manifolds. I will introduce various positivity condtions for such functions and discuss the relationships among them. Examples include globalizable metrics on Hermitian line bundles. A version of the Cauchy-Schwarz inequality for Hermitian symmetric functions and how it relates to complex geometry will be a major part of the talk. To conclude I will pose several accessible problems

Hosts: Peter Ebenfelt and Salah Baouendi

### June 7, 2007

### 11:30 AM

### AP&M 7321

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