11 a.m. - 11:50 a.m. Location: FN 2.102
Texas A&M University
Galois groups in Enumerative Geometry and Applications
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.
Coffee to be served in FN 2.102 at 10:30 AM.
Sponsored by the Department of Mathematical Sciences