Algebra Seminar: Denham -- Rational models for matroids

Graham Denham (University of Western Ontario) 

Friday 17 March, 2:30-3:30pm, Place: Carslaw 375 

Title: Rational models for matroids

Abstract: In favourable conditions, the Leray spectral sequence gives a model,
in the sense of rational homotopy theory, for a hypersurface
complement in a smooth complex variety.  I will describe how this
works for affine, toric and elliptic hyperplane arrangements, where
one obtains a bigraded, differential algebra which captures both the
cohomology of the complement and of a choice of compactification.

The notion of a combinatorial blowup makes it possible to go beyond
geometry and construct a rational model for all matroids, regardless
of whether or not they are realizable by a hyperplane arrangement.  I
will explain why one might want to do so.  This talk is based on joint
work with Christin Bibby and Eva Feichtner.