Sommersemester 2026
08.04.2026 um 13:00 Uhr in 69/E23
Dr. Tal Gottesman (Ruhr-Universität Bochum)
Boolean Antichains and Perfect Modules
Antichains naturally appear in the representation theory of partially ordered sets as they describe submodules of projective indecomposable modules and as such also modules with a simple top. When the poset is moreover a lattice, these modules with simple top have a canonical projective resolution, which unfortunetly might not be minimal.
In this talk I will present different properties on antichains that yield better behaved projective resolutions. These properties were used in a joint work with Kleinau, Klasc and Marczinkik to give a complete classification in lattice theoretic terms of incidence algebras of distributive lattices with pure minimal injective coresolution. This gives interesting examples and non examples to this property introduced by Ajitabh, Smith and Zhang.
15.04.2026 um 13:00 Uhr in 69/E23
Dr. Thor Wittich (Universität Osnabrück)
An Invariant of Algebraic Knots
Algebraic knots are elementary objects of (affine) algebraic geometry which are not understood very well, mostly due to the lack of invariants. In fact, quite some of the biggest problems of the field concern algebraic knots or are strongly related to the existence of algebraic knots with certain properties. Therefore, algebraic knots are of major interest.
We start this talk by giving a playful and visual introduction to (topological) knots and explain how they give rise to algebraic ones. Afterwards, we explain the relevance of algebraic knots wrt. the aforementioned central problems of affine algebraic geometry and summarize the current status of these problems. Finally, we outline how to define an invariant of algebraic knots and how this might lead to a better understanding of algebraic knots. No previous knowledge of topology or algebraic geometry will be assumed, but we expect some appreciation of colorful drawings.
21.04.2026 um 12:15 Uhr in 69/E13
Johannes B. Latzel (Universität Osnabrück)
Geodesics on the Complex Affine Grassmannian Manifold
22.04.2026 um 13:00 Uhr in 69/E23
Hannah Friedman (UC Berkeley)
Metric Algebraic Geometry of the Grassmannian of Lines
The Grassmannian can be realized in many different ways. We focus on two of these: the Pl\”ucker embedding and the projection embedding. The projection embedding of Gr(k,n) is the set of real, symmetric projection matrices of rank k. We illuminate the foundational linear algebra that connects these two embeddings. We introduce the Grassmann distance degree as the algebraic degree of the Euclidean distance problem on subvarieties of the Grassmannian in its projection embedding when the data is also in the Grassmannian. We report on the GD degrees of geometrically meaningful subvarieties. In particular, we characterize the Schubert varieties that have Grassmann distance degree 1. This talk is based on joint work with Andrea Rosana and Bernd Sturmfels.
29.04.2026 um 13:00 Uhr in 69/E23
Elena Hoster (Ruhr-Universität Bochum)
On at least four Polynomial Invariants of Posets
In this talk, I present several invariants that one can associate to a finite, graded, bounded poset. These include the Möbius function, characteristic polynomial, incidence algebra, chain polynomial, ab-index, and (flag) f- and h-vectors.
I will focus on four invariants: (1) the classical ab-index; (2) the extended ab-index; (3) the coarse flag polynomial; and (4) the Chow polynomial. A central theme is that the extended ab-index specializes to each of the others, and can itself be recovered from the classical ab-index. I discuss these relations as well as properties such as their unimodality, log-concavity, gamma-positivity, and real-rootedness.
Based on joint work with Christian Stump and Lorenzo Vecchi.