Graham Denham (University of Western Ontario) - Kirchhoff polynomials and configuration hypersurfaces

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, and this provides some incentive to study the motives and periods arising from the projective hypersurface cut out by such a polynomial.

From the geometric perspective, work of Bloch, Esnault and Kreimer (2006) suggested that the most natural object of study is a polynomial determined by a linear matroid realization, for which the Kirchhoff polynomial is a special case.

I will describe some ongoing joint work with Delphine Pol, Mathias Schulze, and Uli Walther on the interplay between geometry and matroid combinatorics for this family of objects.