##### Department of Mathematics,

University of California San Diego

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### 2009 Southern California Optimization Day

## Martin Harrison

#### UCSB

## Minimal Sums of Squares in a free *-algebra

##### Abstract:

In this talk, I discuss the reduction of the number of squares needed to express a sum of squares in the free *-algebra R. I will give examples of sums which are irreducible in this sense, and prove bounds on the minimal number of terms needed to express an arbitrary sum of squares of a given degree in a given number of variables

### March 19, 2009

### 11:00 AM

### AP&M 6402

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