##### Department of Mathematics,

University of California San Diego

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### Math 248 - Analysis

## Imre Patyi

#### UCSD Visitor

## Towards an analog of Stein theory in infinite dimensions

##### Abstract:

Simply put, a Stein manifold is a closed complex submanifold of complex Euclidean space. Stein manifolds have rich function theory and many of their global properties can be understood with the help of sheaf cohomology. As a long term goal we would like to prove vanishing theorems for closed submanifolds of Hilbert spaces, and give a cohomological characterization of these submanifolds. In this talk we survey the available results in this direction and look at the possible near future.

Host: Peter Ebenfelt

### December 2, 2003

### 9:30 AM

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