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Enumerative, Algebraic and Geometric Aspects of Arrangements

International Workshop

Date: Thursday, August 25th, 2016
Time: 09:00-17:00
Place:Universität Bremen, MZH 7200 (the thesis defense will take place in Cartesium/Rotunde)

Michele d'Adderio (Université Libre de Bruxelles)
Pauline Bailet (Universität Bremen)
Matthias Lenz (Université de Fribourg)
Sonja Riedel (Universität Bremen / Université de Fribourg)
Masahiko Yoshinaga (Hokkaido University)


09:00-10:00Masahiko Yoshinaga (Hokkaido University)
The Euler characteristic reciprocity for order polynomials
It is well known that the Euler characteristic can be considered as a generalization of the notion of cardinality of finite sets. We will apply the above idea to the study of "combinatorial reciprocity", and formulate a reciprocity at the level of Euler characteristics. This talk is based on the joint work with Takahiro Hasebe. (
10:30-11:30Michele d'Adderio (Université Libre de Bruxelles)
The sandpile model on complete bipartite graphs
We will dicuss some algorithmic and some enumerative aspects of the object in the title. The talk has virtually no prerequisites, so it will be accessible to anybody (also students!) willing to attend.
13:00-13:30Matthias Lenz (Université de Fribourg)
A convolution formula for Tutte polynomials of arithmetic matroids and other combinatorial structures
A lot of combinatorial and topological information about a hyperplane arrangement is captured by the underlying matroid and in particular by its Tutte polynomial. In the 1990s,  Kook-Reiner-Stanton and Etienne-Las Vergnas proved a convolution formula for the Tutte polynomial of a matroid. Recently, D'Adderio-Moci introduced a combinatorial structure called arithmetic matroid that captures combinatorial and topological information about a toric arrangement, i.e. an arrangement of subtori of codimension one on a torus. In this talk, we will generalise the convolution formula for the Tutte polynomial to a setting that includes Tutte polynomials of arithmetic matroids, delta-matroids, and polymatroids. As corollaries, we obtain new proofs of two positivity results for pseudo-arithmetic matroids, a combinatorial interpretation of the arithmetic Tutte polynomial in terms of arithmetic flows and colourings and a connection with lattice point counting in zonotopes.
This is joint work with Spencer Backman.
13:45-14:15Pauline Bailet (Universität Bremen)
Monodromy of the Milnor fiber of sharp arrangements
In this talk we study the first homology group of the Milnor fiber of sharp arrangements in the real projective plane (more precisely, the decomposition into eigenspaces of the monodromy operator). We describe an algorithm which relies on a minimal complex of the deconing arrangement and its boundary map, and computes possible eigenvalues of the monodromy. After some basic recap on Milnor fiber monodromy and the minimality of the complement, I will give a criterion to prove a-monodronicity. (This is joint work with Simona Settepanella)
15:15-16:30Sonja Riedel (Universität Bremen / Université de Fribourg)
Combinatorial Invariants of Toric Arrangements
Thesis defense

Copyright: ALTA, 2016.