FB 6 Mathematik/Informatik

Institut für Mathematik

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Wintersemester 2013/14

9.10.2013 um 16:15 Uhr in 69/125:

Dr. Lukas Katthän (Universität Osnabrück)

On homology spheres with few minimal non-faces

Let Δ be a (d − 1)-dimensional homology sphere on n vertices with m minimal non-faces. We consider combinatorial properties of the system of minimal non-faces. In particular, we show that for a fixed value of α(Δ) := m − (n − d), there are only (essentially) finitely many homology spheres. For the proof, we use the fact that the Stanley-Reisner ring of Δ is Gorenstein.

12.11.2013 um 16:15 Uhr in 69/125:

Dr. Fatemeh Mohammadi (Universität Osnabrück)

Syzygies of matroid ideals

We discuss natural ideals associated to matroids, and their syzygies in terms of combinatorics of the matroid. We show that the last Betti number counts the number of 'no broken circuits' of the matroid. In particular, for graphic matroids, we describe the Betti numbers in terms of the number of acyclic orientations of the graph (with the unique q).

19.11.2013 um 16:15 Uhr in 69/125:

Daniela Anca Macinic (Romanian Academy)

Combinatorics in the topology of complex hyperplane arrangements

We discuss the combinatorial nature of various topological invariants of the complement of a complex hyperplane arrangement, such as the homotopy groups of the complement. We present results concerning arrangements of lines in the complex projective plane with simetric structures of type (p,q)-net.

03.12.2013 um 16:15 Uhr in 69/125:

Ulrich von der Ohe (Universität Osnabrück)

The method of de Pron

We present the classical Prony-method for parameter estimation in exponential sums and a recent generalization by Plonka and Peter.

10.12.2013 um 16:15 Uhr in 69/125:

Richard Sieg (Universität Osnabrück)

Scheduling Sport Tournaments and Monoids

A round-robin tournament consists of an even number of teams 2n, each playing against every other team exactly once with n games per day. Given a home-away-pattern for such a tournament, we want to check whether it is feasible, i.e. whether there exists a schedule for the tournament that is compatible with the pattern. We present a conjecture by Briskorn, saying that it is sufficient for this problem to check a certain linear program for feasibility. Next we discuss an equivalent conjecture about specific integrally closed parts of a certain monoid and present first results using the software normaliz.

21.01.2014 um 16:15 Uhr in 69/125:

Dr. Ismaël Soudères (Universität Osnabrück)

Combinatorial structures of moduli spaces of curves of genus 0

In this talk, I will present the moduli spaces of curves M0,n and their Deligne-Mumford compactification. This presentation will concentrate on showing the various combinatorial properties underlying the geometry of this spaces: representation of the boundary by trivalent trees, descritpion of the various symmetries, introduction of the Stasheff's polytop, etc.