Geometry Seminar

Date: September 16, 2022

Time: 4:00PM - 4:50PM

Location: BLOC 302

Speaker: Thomas Yahl, Texas A&M University

Title: Computing Galois groups of Fano problems

Abstract: A Fano problem consists of enumerating linear spaces of a fixed dimension on a variety, generalizing the classical problem of the 27 lines on a smooth cubic surface. Those Fano problems with finitely many linear spaces have an associated Galois group that acts on these linear spaces and controls the complexity of computing them in coordinates via radicals. Galois groups of Fano problems have been studied both classically and modernly and have been determined in some special cases. We use computational tools to prove that several Fano problems of moderate size have Galois group equal to the full symmetric group, all of which were previously unknown.