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

Venue: 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.