Kushnirenko's Theorem

Student Algebraic Geometry Seminar
Friday, November 17, 2017 - 10:00
1 hour (actually 50 minutes)
Skiles 114
GA Tech
Motivated by the general problem of polynomial system solving, we state and sketch a proof Kushnirenko's theorem. This is the simplest in a series of results which relate the number of solutions of a "generic" square polynomial system to an invariant of some associated convex bodies. For systems with certain structure (here, sparse coefficients), these refinements may provide less pessimistic estimates than the exponential bounds given by Bezout's theorem.