##### Department of Mathematics,

University of California San Diego

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### Food For Thought Seminar

## David Scheinker

#### UCSD

## Bounded analytic functions of several complex variables

##### Abstract:

\indent Function theory of several complex variables is much less well understood than function theory of functions of one variable. One approach to attempting to bridge this divide is to study an analytic function $f$ on $D^n$ as follows. Fix a 1-dimensional algebraic variety $V\subset C^n$ and let $F$ denote the restriction of $f$ to $V$. Since $V$ is 1-dimensional, $F$ behaves somewhat like a function of one complex variable and we could potentially apply the theory of functions of one variable to understanding $F$. If we can use this approach to prove facts about $F$, then we could potentially extend some of these results to $f$. In particular, we take this approach to generalize to $D^n$ the classic Schwarz Lemma on the disc $D$. Familiarity with the definition of an analytic function of one variable is the only thing that will be assumed.

### February 17, 2011

### 10:00 AM

### AP&M 7321

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