Numerical computation of Newton polytopes

by Frank Sottile

The Newton polytope of a polynomial f is a combinatorial approximation to f that 
also encodes much information about the hypersurface H defined by f.  In this talk, 
I will address the problem of how to recover the Newton polytope (or even f) when
H is represented numerically via a witness set, which is a data structure capturing
the notion of a generic point of H.   This talk will describe witness sets and how
such a representation may arise without knowledge of f, explain an algorithm for 
solving this problem, and how it was used to find a face of the Lueroth invariant.

This is joint work with Jon Hauenstein