Current Topics Seminar
| Speaker | Rekha Thomas |
| Title | Real Roots of Polynomial Systems |
| Date | April 16 4:00pm PDL C-36 |
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How hard can it be to find one or all real roots to a system of polynomial equations, or to count or bound the number of such roots? Unlike for complex roots, these are all surprisingly difficult tasks and yet of great importance in applications all over science and engineering. In this talk I will explain some of the (few existing) theorems about real roots starting with the classical Descarte's rule of signs. Unlike Hilbert's Nullstellensatz for complex solutions from 1893, the real Nullstellensatz was formulated only in the 1960s. The highlight will be Bernstein's theorem from the 1970s that makes a surprising connection to discrete geometry.
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