Seminar

Frank Sottile: "Galois groups in Enumerative Geometry"

Abstract:  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 of many to compute, study, and use Galois groups of geometric problems, including those that arise in applications of algebraic geometry.

Mats Boij: "The Kähler package for finite geometries and modular lattices"

In this joint work with Bill Huang, June Huh and Greg Smith we give very explicit proofs of the existence of a Kähler package for the graded Möbius algebra associated to the lattice of subspaces of a vector space over a finite field $\mathbb F_q$. There are fascinating connections to other areas such as the theory of Gelfand pairs and generalized Radon transforms.