New perspectives on hyperplane arrangements
The conference "New perspectives on hyperplane arrangements" will take place on May 12-16, 2025 in Bochum.
There will be seven scientific talks:
Speaker | Title |
---|---|
Takuro Abe (Tokyo) | Tame arrangements |
Xiangying Chen (Bochum) | |
Daniele Faenzi (Bourgogne) | |
Lukas Kühne (Bielefeld) | |
Shota Maehara (Kyushu) | Use of matrix for exponents of 2-dimensional multiarrangements |
Paul Mücksch (Berlin) | Fibrations for hyperplane arrangements and oriented matroids |
Leonie Mühlherr (Bielefeld) | Connected hypersubgraph arrangements |
Piotr Pokora (Krakow) | A new hierarchy for line arrangements |
Sven Wiesner (Bochum) |
Registration
TBA
Dates and Program
TBA
Venue
The venue for the conference will be Beckmanns Hof in the Botanical Garden south of the RUB campus. The talks will be held in room Tokio. The directions to Beckmanns Hof are indicated at the bottom center of the campus map here. It is advised to follow the directions on the signs in the area.
Funding & Accomodation
TBA
Abstracts
Takuro Abe
Tame arrangements
Tame arrangements were informally introduced by Orlik and Terao for the study of Milnor fibers of arrangements. The definition of tame arrangements are based on projective dimensions, and in general it is very hard to check. However, tame arrangements have played important roles in several areas of arrangements, including freeness, master functions and critical varieties, Bernstein-Sato polynomials, Solomon-Terao algebras, likelihood geometry and so on. On the other hand, the research on tame arrangements themselves was very few, like a sufficient condition for tamenss by Mustata-Schenck.
In this calk, we give several fundamental results for tameness, i.e., addition, deletion and restrictions, Zeigler-Yoshinaga type results for tameness. We also give several examples of tame arrangements by using them.
Xiangying Chen
TBA
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Daniele Faenzi
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Lukas Kühne
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Shota Maehara
Use of matrix for exponents of 2-dimensional multiarrangements
At once Max Wakefield and Sergey Yuzvinsky utilized some square matrix for the research of exponents of 2-dimensional multiarrangements. It is famous that they proved "for a fixed balanced multiplicity on 2-dimensional arrangement, the exponents is closest in general positions" by using such matrix. In this talk, we introduce a matrix almost similarly as Wakefield and Yuzvinsky do and consider further application for exponents. In fact, exponents of 2-dimensional multiarrangements can be calculated by checking whether the corresponding matrices have full rank or not. Especially, we show some results about exponents of multiarrangements whose underlying arrangements consist of four lines, almost only considering row basic transformations.
Paul Mücksch
Fibrations for hyperplane arrangements and oriented matroids
In the topological study of hyperplane arrangements fibrations play an important role. On the one hand, complex complements of certain arrangements might be realized as fibre bundles over complements of other arrangements leading to solutions of the K(pi,1)-problem in these instances. On the other hand, the Milnor fibration of a complex arrangement is a much studied geometric invariant but there are still many open questions about the topology of its fibres. In my talk I will present new results connecting such fibrations with the combinatorics of oriented matroids. This is partly joint work with Masahiko Yoshinaga.
Leonie Mühlherr
Connected hypersubgraph arrangements
In a recent work, Cuntz and Kühne defined the class of connected subgraph arrangements. This includes the resonance arrangement and some ideal subarrangements of Weyl arrangements. They studied among other things the freeness and simpliciality of these arrangements and found graph theoretical criteria for these properties. In this project, we want to extend the definition of these arrangements to hypergraphs and study the aforementioned properties in order to generalize the characterizations established by Cuntz and Kühne. This talk gives an introduction to the connected subgraph arrangements, explains the generalization idea, presents results pertaining to freeness of this arrangement class and shows an interesting connection to Boolean buildingssets.
Piotr Pokora
A new hierarchy for line arrangements
The main goal of my talk is to explain the notion of type for plane curves, which is equal to the initial degree of the corresponding Bourbaki ideal. After introducing all the necessary definitions, we present basic properties of this invariant and show that it behaves well with respect to the unions. It turns out that the curves of type 0 are exactly the free curves and the curves of type 1 are the plus-one generated curves. The third natural class of curves that appears in our investigations is the class of curves of type 2. There are exactly two subclasses of curves of type 2, called curves of type 2A and 2B, and then we show how to construct infinite families of line arrangements of type 2A and 2B and we show that curves of type 2 show up during the studies on Ziegler pairs. The talk is based on joint work with Takuro Abe and Alex Dimca.
Sven Wiesner
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