Polynomial equations and polyhedra
Introductory Workshop: Geometric and Topological Combinatorics September 05, 2017 - September 08, 2017
Location: MSRI: Simons Auditorium
52B20 - Lattice polytopes (including relations with commutative algebra and algebraic geometry) [See also 06A11, 13F20, 13Hxx]
I will discuss how Newton polyhedra and their generalizations are used to study solutions of systems of polynomial equations. For polynomials with generic coefficients, we can tell from the Newton polytopes whether the solution set is empty, how many solutions there are if finite, and whether the solution set is irreducible. We will also see tropical varieties, resultants, and polyhedral homotopies.
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