Graham Denham - Geometry and Combinatorics (Math)
Room: 108
Graham Denham (Western University)
Title: Singular loci of configuration hypersurfaces
Abstract: A finite graph determines a Kirchhoff polynomial, which is a squarefree, homogeneous polynomial in a set of variables indexed by the edges. The Kirchhoff polynomial appears in an integrand in the study of particle interactions in high-energy physics, which provides some incentive to study the motives and periods arising from the projective hypersurface cut out by such a polynomial.
From this perspective, work of Bloch, Esnault and Kreimer (2006) suggested that the more natural object of study is, in fact, a polynomial determined by a hyperplane arrangement, which is closely related to the basis generating polynomial of the associated matroid. I will describe joint work with Mathias Schulze and Uli Walther on the singular loci of such polynomials.