Roberto Pagaria: Arithmetic matroids and their representations

Abstract:
In this talk we will define matroids and orientable matroids and we will relate them to well-studied topological objects: hyperplane arrangements. Our aim is to describe the analogous theory of arithmetic matroids and toric arrangements.
We will give the definition of arithmetic matroids and discuss the representability problem, which is closely related to the orientability of the arithmetic matroid. Finally, we will analyse the relation between arithmetic matroids and toric arrangements by considering the cohomology algebra of the complement of the arrangement. Unfortunately, the picture is not as rosy as in the case of hyperplanes.