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Emanuele Delucchi: On the combinatorics of Abelian arrangements

Time: Wed 2019-04-10 10.15 - 11.00

Location: Room 3418, Lindstedtsvägen 25. Department of Mathematics, KTH

Participating: Emanuele Delucchi (University of Fribourg)

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Abstract: Arrangements of hyperplanes have long offered a geometric point of view on (representable) matroids from which many a development in matroid theory has been inspired. The theory of arrangements recently broadened its scope beyond the linear case to include arrangements in the torus, in products of elliptic curves and, more generally, in Abelian Lie groups. This spurred the search for a suitable extension of matroid theory. In this expository talk I will define Abelian arrangements and briefly survey the state of the art, from a topological-geometrical as well as from a combinatorial point of view.    Then, I will outline the foundations of a new theory of group actions on posets. I will present some of the new results that it allows us to obtain, while highlighting the unifying point of view that it gives on the existing literature. I will especially focus on applications to the (still not well understood) structure of intersection posets of abelian arrangements and on commutative-algebraic aspects of the theory.   The material is partly drawn from joint works with Alessio D’Alì, Giacomo d’Antonio, Noriane Girard, Giovanni Paolini and Sonja Riedel.