Cluster Geometry Lab Weekly Workshop: Arina Voorhaar

Newton polytopes, sparse resultants and enumeration of singularities

We will discuss the following two problems, arising in elimination theory in the context of Newton polytopes. The first one is to compute the signs of the leading coefficients of the sparse mixed resultant. The second problem concerns the singular points of a plane projection of a complete intersection curve given by a generic system of polynomials with given support. In a broader sense, the talk is devoted to new methods of enumeration of singularities which arise naturally in the context of Newton polytopes and sparse polynomials. As an application of the obtained methods we describe the Newton polytope of the Morse discriminant — the closure of the set of all non-Morse polynomials of a given degree.