Tropical Bernstein's theorem
- Series
- Tropical Geometry Seminar
- Time
- Wednesday, October 27, 2010 - 10:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 114
- Speaker
- Anton Leykin – Georgia Tech
The classical Bernstein's theorem says that the number of roots of a system of sparse polynomials with generic coefficients equals the mixed volume of the Newton polytopes of the polynomials. We shall sketch a constructive proof by describing the solutions in the field of Puiseux series. The tropical Bernstein's theorem says that the number of tropical roots of a system of sparse tropical polynomials with generic coefficients equals the mixed volume of the Newton polytopes. We will prove this using the Huber--Sturmfels method for computing mixed volumes with regular mixed subdivisions of polytopes. Side topics: computation of mixed volumes, polyhedral homotopy continuation (finding complex solutions of a sparse polynomial system).