##### Department of Mathematics,

University of California San Diego

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### Math 295 - Mathematics Colloquium

## Mihai Putinar

#### UCSB

## Matrix positivity preservers in fixed dimension

##### Abstract:

A celebrated 1942 result of Schoenberg characterizes all entry-wise functions which preserve positivity of matrices of any size. I will present a characterization of polynomials which preserve positivity when applied entry-wise on matrices of a fixed dimension. All put in historical context and motivated by recent demands of statistics of large data and optimization theory. A sketch of the proof will take a detour through the representation theory of the symmetric group.

Hosts: Bill Helton and Jiawang Nie

### May 14, 2015

### 4:00 PM

### AP&M 6402

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