Title: Galois groups in Enumerative Geometry and Applications

Date: 10/12/2017

Time: 4:10 PM - 5:00 PM

Place: C304 Wells Hall

Speaker: Frank Sottile, Texas A&M University

In 1870 Jordan explained how Galois theory can be applied
to problems from enumerative geometry, with the group encoding intrinsic structure of the problem. Earlier Hermite showed the equivalence of Galois groups with geometric monodromy groups, and in 1979 Harris initiated the modern study of Galois groups of enumerative problems. He posited that a Galois group should be `as large as possible' in that it will be the largest group preserving internal symmetry in the geometric problem.
I will describe this background and discuss some work
in a long-term project to compute, study, and use Galois
groups of geometric problems, including those that arise
in applications of algebraic geometry. A main focus is
to understand Galois groups in the Schubert calculus, a
well-understood class of geometric problems that has long
served as a laboratory for testing new ideas in enumerative
geometry.