Tentative Schedule

 

Titles and abstracts of talks
updated 18.05.2026

Michael Cuntz
Title: Simplicial arrangements with special vertex.
Abstract: I introduce a general class of arrangements that includes several known types of finite and infinite arrangements. In the special case of simplicial arrangements I obtain a classification result.

Michael DiPasquale
Title: Multi-braid arrangements and free resolutions
Abstract: Freeness of multi-arrangements is an important topic due to Ziegler’s freeness criterion. A special case of interest is free multiplicities on braid arrangements. A seminal result of Terao shows that a constant multiplicity is free (on any Coxeter arrangement). In their ground-breaking work introducing addition-deletion methods for multi-arrangements, Abe-Terao-Wakefield prove that multiplicities which satisfy inequalities arising from a supersolvable filtration are free (let us call these \textit{supersolvable multiplicities}). Abe-Nuida-Numata additionally prove that a large class of multiplicities on braid arrangements — which we refer to as ANN multiplicities — are free (indeed, inductively free). In joint work with C. Francisco, J. Mermin, and J. Schweig, we proved that the only free multiplicities on the $A_3$ braid arrangement are the ANN multiplicities and the supersolvable multiplicities. This characterization partially generalizes, but the classification of free multiplicities on higher braid arrangements is still incomplete. In this talk, I explain a connection between free multiplicities on braid arrangements and free resolutions of certain power ideals. This yields an additional obstruction to free multiplicities on braid arrangements.

Marco Golla
Title: Complex curves from a symple(ctic) perspective
Abstract: I will give a gentle introduction to pseudo-holomorphic curves in the complex projective plane. The purpose is twofold: on the one hand, to describe some symplectic tools that can be used to study
complex curves, and on the other to present some open questions on pseudo-holomorphic curves that one can borrow from the complex (real) theory.

Dante Luber
Title: Computations and applications with singular matroid realization spaces
Abstract: A matroid is said to be realizable if there exists a hyperplane arrangement whose intersection lattice is isomorphic to the lattice of flats of the given matroid. The moduli space of all hyperplane arrangements corresponding to a matroid M is known as the realization space of M. Mnev Universality tells us that realization spaces of rank 3 matroids can be arbitrarily singular. However, Mnev’s result relies on a constructive algorithm which leads to few concrete examples. This talk will cover a sequence of projects related to the geometry of matroid realization spaces. We will use OSCAR to isolate examples of matroids whose realization spaces are singular, and classify the singularities we find. We will also discuss derivation modules of hyperplane arrangements, and exhibit matroids and hyperplane arrangements where the geometry of the realization space relates to the properties of the derivation modules. We will conclude with a demonstration of the relevant software.

Leonie Mühlherr
Title: On the interplay of combinatorics and algebra in graphic arrangement theory.
Abstract: Besides being thoroughly combinatorial objects themselves, some hyperplane arrangement classes have very natural ties to other parts of this field. For example, the subarrangement of the braid
arrangement can be associated to a simple graph and thus be analysed through the lense of graph theory. One can also associate hyperplanes to the sets of a given buildingset and consider their arrangement.
This talk will exemplify this connection of arrangements to combinatorial objects through algebraic research questions pertaining to the module of logarithmic derivations, specifically in the case where
the module and thus the arrangement is free.

Sakumi Sugawara
Title: Topological invariants of combinatorial line arrangements
Abstract: A combinatorial line arrangement is an abstraction of the combinatorial structure of line arrangements in a projective plane, which is equivalent to the notion of a simple matroid of rank three. In this talk, we will discuss two recent topological results on combinatorial line arrangements.
First is the description of the cohomology ring of the boundary manifold. Since the boundary manifold of a complex line arrangement is conbinatorially constructed, it is defined over any combinatorial line arrangements. We will show the doubling formula for the cohomology ring of the boundary manifold for any combinatorial line arrangements, which is originally proved by Cohen-Suciu for complex realizable case.
Second is on topological realizations of combinatorial line arrangements, which is defined as an arrangement of embedded 2-spheres in the complex projective plane. We will show that the cohomology ring is isomorphic to the Orlik-Solomon algebra, as ordinary line arrangements. On the other hand, we construct a topological realization whose complement fails to be minimal, unlike ordinary line arrangements.

Ryo Uchiumi
Title: Equivariant version of characteristic quasi-polynomials and root systems
Abstract: In this talk, we introduce an equivariant version of characteristic quasi-polynomials as the permutation characters on the complement of mod q hyperplane arrangements.
We show that its character is a quasi-polynomial in q and it is also closely related to the equivariant version of Ehrhart quasi-polynomials. We will also present some of computation of equivariant characteristic quasi-polynomials of root systems. We show equivariant-theoretic refinements of the beautiful properties of characteristic quasi-polynomials of root systems.

Masahiko Yoshinaga
Title: What does the real structure of a hyperplane arrangement tell us?
Abstract: The real structure of a hyperplane arrangement is directly related to many interesting things. For example, it provides combinatorial structures (oriented matroids, intersection poset, adjacent graphs, etc), topological information (Betti numbers, Salvetti complex, homotopy groups, etc), and algebraic structure (Varchenko-Gelfand algebra).
We survey some of these connections. (This talk is partially based on joint work with Yukino Yagi.)

Francesca Zaffalon
Title: Generalizing self-duality in the Grassmannian
Abstract: Self-dual point configurations have been studied throughout the centuries. In this talk, I will introduce a generalization of these configurations: self-projecting point configurations. These points are parametrized by a subvariety of the Grassmannian, called self-projecting Grassmannian. I will describe how small self-projecting Grassmannians relate to classical moduli spaces, such as moduli spaces of pointed genus g curves. In the second part of the talk, self-projectivity will be studied from the combinatorial point of view of matroids. In particular, we will introduce self-projective matroids and study their realizability inside the self-projective Grassmannian. I will end with experimental results for the computation of such realization spaces. Based on joint work with Alheydis Geiger.