## University of Sydney Algebra Seminar

# Graham Denham (University of Western Ontario)

## Friday 17 March, 14:30-15:30pm, Place: Carslaw 375

## Rational models for matroids.

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.