## Seminar:

Spring 2013, Thursdays, Milner 216, 4:00-4:50 PM
__ Date:__ **March 28 **

**" Non-negative Polynomials and Sums of Squares "**

**Kaitlyn (Hellenbrand) Phillipson**

__Abstract__Polynomials that are non-negative over the reals were the subject of Hilbert's 17th problem. It is easy to see that a polynomial that is written as a sum of squares is non-negative, but the converse is not always true. In this talk, we will discuss the background of this problem, as well as recent results concerning the probability that a non-negative polynomial can be written as a sum of squares. No prior knowledge of algebraic geometry is necessary for this talk.