Скачать или смотреть Seminar on Applied Geometry and Algebra (SIAM SAGA): Frank Sottile

Date: Tuesday, August 10

Speaker: Frank Sottile, Texas A&M

Title: Applications of Bernstein's Other Theorem

Abstract: Many of us are familiar with Bernstein's Theorem giving the number of solutions in the torus to a general system of sparse polynomial equations. The linchpin of his proof is what I like to call Bernstein's Other Theorem, which describes exactly when a system fails to be general in the above sense (Bernstein-general). His bound is a simple consequence of this using, for example, the characterization of mixed volume.

Polynomial systems in nature are rarely general given their supports, and thus Bernstein's Theorem is only a priori a bound for their number of solutions. Nevertheless, a surprising number of polynomial systems from applications do achieve Bernstein's bound. For such a system, the polyhedral homotopy give an optimal algorithm for computing its solutions. My talk will discuss this background and give some polynomial systems from applications which are not general given their support, but are Bernstein-general.