Oberseminar Algebra, Zahlentheorie und Diskrete Mathematik
Sommersemester 2026
Donnerstags, 14:15-15:15 Uhr
Seminarraum A410 im Welfenschloss (Hauptgebäude, Welfengarten 1)
| Datum | Vortragende/r | Vortragstitel |
|---|---|---|
| 30.04.2026 | Antoine de St. Germain (University of Hong Kong) | Mordell-Schinzel surfaces and cluster algebras (online) The set of positive integer points of the celebrated Markov surface admits the structure of a 3-regular tree. Much later, it was understood that this tree has a natural cluster algebraic interpretation. In this talk, I will first introduce a family of surfaces called Mordell-Schinzel surfaces and show that their positive integer points have a graph structure with a natural cluster algebraic interpretation. I will then explain how the structure theory of cluster algebras translates into a resolution of interesting (and often difficult !) arithmetic questions. I will not assume any knowledge about Mordell-Schinzel surfaces or about cluster algebras. This is partly based on ongoing joint work with Robin Zhang (MIT). |
| 07.05.2026 | Michael Cuntz (LUH) | Frieze patterns and simplicial arrangements Arrangements of lines which triangulate the plane, the so-called simplicial arrangements, appear to be rare. They have been collected during the last 80 years. It is conjectured that they are all known. In my talk I will explain a relation between simplicial arrangements and frieze patterns. |
| 21.05.2026 | Jan Stricker (Frankfurt) | Pseudo Root Systems and Simplicial Hyperplane Arrangements Root systems are sets of vectors, which elegantly describe all finite reflection groups. Dimitrov and Fioresi discovered generalized root system, whose short definition generalizes the concept of the classical root systems. Indeed the corresponding hyperplane arrangements are still simplicial hyperplane arrangements and Cuntz and Mühlherr classified them to be the Weyl arrangements and their restrictions. We generalize the Dimitrov and Fioresis root systems to pseudo root systems. The hyperplane arrangements of pseudo root systems are still simplicial hyperplane arrangements. We prove that pseudo root system are closed under restriction and localization and all reflection arrangements and their restrictions have pseudo root systems.Furthermore, we show that there are only finitely many 3-dimensional pseudo root systems and more simplicial hyperplane arrangements with pseudo root systems then restrictions of reflection arrangements. |
| 18.06.2026 | Rene Marczinzik (Bonn) | |
