Combinatorial Algebraic Geometry

Date: March 1, 2019

Time: 11:00AM - 11:50AM

Location: Bloc 605AX

Speaker: Taylor Brysiewicz, Texas A&M University

Title: Solving equations using monodromy

Abstract: Given a zero-dimensional parametrized polynomial system in variables x and parameters c the projection f : X -> C_c forms a branched cover where the fibre over any parameter c′ is the finite set of solutions to the system restricted to c′. If D is the branch locus of this map, the fundamental group pi_1(C_c-D,c′) based at c′ acts on the fibre over c′ via analytic continuation which induces a set of permutations called the monodromy group of f.

While the computations of monodromy groups are interesting in their own right, leveraging the monodromy group to compute the fibres of f has proven to be quite effective. Recently, there has been serious improvements to monodromy solving algorithms and software. I will discuss these monodromy algorithms as well as their applications.