MATH Seminar
| Title: Polynomials non-negative on non-compact semialgebraic sets |
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| Seminar: Algebra |
| Speaker: Ha Nguyen of Emory University |
| Contact: Vicki Powers, vicki@mathcs.emory.edu |
| Date: 2009-09-28 at 4:00PM |
| Venue: MSC W303 |
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| Abstract: Recently, M. Marshall answered a long-standing question in real algebraic geometry by showing that if $f(x,y) \in \mathbf{R}[x,y]$ and $f(x,y) \geq 0$ on the strip $[0,1] \times \mathbf{R}$, then $f$ has a representation $f = \sigma_0 + \sigma_1 x(1 - x)$, where $\sigma_0, \sigma_1 \in \mathbf{R}[x,y]$ are sums of squares. In this talk, we give the background to this result, which goes back to Hilbert's 17th problem, and our generalizations to other non-compact basic closed semialgebraic sets of $\mathbf{R}^2$ which are contained in strip. We also give some negative results. |
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