abstract: ecent work of De Concini, Procesi and Vergne on the vector partition function spurred many different directions of research. One such direction focuses on the topology of toric arrangements, another is the study of arithmetic matroids and other algebro-combinatorial structures.
In this talk I will suggest a way to establish a unifying structural framework for these two directions by considering group actions on semimatroids. On the one hand, this generalizes some important aspects of the combinatorial topology of toric arrangements; on the other hand it gives rise to new examples of abstract arithmetic matroids endowed with natural “geometric" data.