|09:00-10:00||Masahiko 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.
|10:30-11:30||Michele 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.|
|13:00-13:30||Matthias 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.
|13:45-14:15||Pauline 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)|
|15:15-16:30||Sonja Riedel (Universität Bremen / Université de Fribourg)|
|Combinatorial Invariants of Toric Arrangements|