Title: Counting complex solutions of polynomial equations via Newton polytopes
Speaker: Prof. Jugal Verma (IIT, Bombay)
Date: 05 September 2017
Time: 2:30 - 3:45 and 4:00 - 5:00 pm
LH-1, Mathematics Department
We shall discuss a theorem of Bernstein published in
1975 about the number of common solutions of n complex polynomials in n
variables in terms of the mixed volumes of their Newton polytopes.
This is a far reaching generalisation of the Fundamental Theorem of
Algebra and Bezout’s Theorem about intersections of plane algebraic
curves. If time permits, we shall sketch a proof of Bernstein’s theorem
using Hilbert functions of monomial ideals in polynomial rings.