Baker-Lorscheid (Hyperfield) Multiplicities in Two Variables

Algebra Seminar
Tuesday, April 12, 2022 - 12:00pm for 1 hour (actually 50 minutes)
Skiles 006
Trevor Gunn – Georgia Tech –
Ashley Wheeler

For polynomials in 1 variable, Matt Baker and Oliver Lorschied were able to connect results about roots of polynomials over valued
fields (Newton polygons) and over real fields (Descartes's rule) by looking at factorization of polynomials over the tropical and signed
hyperfields respectively. In this talk, I will describe some ongoing work with Andreas Gross about extending these ideas to two or more
variables. Our main tool is the use of resultants to transform questions about 0-dimensional systems of equations to factoring a single
homogeneous polynomial.