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.
06.05.2026 um 13:00 Uhr in 69/E23
Joris Köfler (MPI MiS Leipzig)
Adjoints and Positive Geometries with Positive Genus
Adjoints are a powerful combinatorial tool to compute canonical forms of positive geometries. Using adjoints we construct a positive geometry, which makes a genus one pair, in the new framework by Brown and Dupont. Based on joint work with Dmitrii Pavlov and Rainer Sinn.
08.05.2026 um 14:00 Uhr in 69/117
Veronica Calvo Cortes (MPI Leipzig)
Positive Charts of Toric Varieties and Stringy Integrals
We construct affine charts of a smooth projective toric variety which contain its nonnegative points, and which admit a closed embedding into the total coordinate space of Cox's quotient construction. We show that such positive charts arise from smooth subcones of the nef cone. To each positive chart we associate an algebraic moment map, the fibers of which are the critical points of a monomial function in Cox coordinates. This work provides a toric framework for the theory of u-equations in positive geometry. I will also discuss some generalisations of string integrals which are a motivation for our construction. This is joint work with Simon Telen.
08.05.2026 um 15:00 Uhr in 69/117
Mieke Fink (Universität Osnabrück)
Duals of Cosmological Polytopes
The canonical form of a polytope can be expressed in terms of the volume of its dual polytope. In this talk, I will present two triangulations of the dual cosmological polytope, which allow us to compute the canonical form of the cosmological polytope in two ways. This is based on joint work with Anna Birkemeyer, Torben Donzelmann and Martina Juhnke.
08.05.2026 um 16:00 Uhr in 69/117
Prof. Dr. Bernd Sturmfels (MPI Leipzig)
Positive Geometries from Cubic Surfaces
13.05.2026 um 13:00 Uhr in 69/E23
Steffen Schlie (Universität Osnabrück)
Boundary $h^\ast$-vectors and unimodular triangulations
We study the Ehrhart $h^\ast$-polynomial of (the boundary of) a lattice polytope via regular unimodular triangulations and Gr\"obner degenerations of toric ideals. Our main result is a boundary analogue of the well-known Sturmfels correspondence. This allows us to connect the boundary $h^\ast$-polynomial to the $h$-polynomial of any regular unimodular triangulation, in analogy to the classical Betke-McMullen Theorem.
Providing a direct link between Ehrhart theory and the face enumeration of simplicial complexes, we then transfer structural results from the theory of simplicial polytopes to the setting of lattice polytopes. In particular, we derive general Dehn-Sommerville-type relations between $h^\ast(P)$ and $h^\ast(\partial P)$. Under the additional assumption of $\partial P$ admitting a regular unimodular triangulation, we recover old and prove new characterization results concerning symmetry or unimodality, as well as upper and lower bounds for coefficient-wise differences within $h^\ast(P)$.
20.05.2026 um 13:00 Uhr in 69/E23
Kevin von Bargen (Universität Osnabrück)
Evaluating Training Strategies for Physics-Informed Neural Networks
Physics-informed neural networks (PINNs) approximate solutions of partial differential equations by minimizing residuals of the governing equations and auxiliary conditions over a neural-network hypothesis class. This perspective raises practical questions about how the resulting optimization problem is constructed and how realizations of training pipelines are compared. The talk gives a mathematical introduction to PINNs and discusses principles for evaluating their training strategies.
27.05.2026 um 13:00 Uhr in 69/E23
Jhon Bladimir Caicedo Portilla (Universität Osnabrück)
Ehrhart-Theoretic Aspects of Sylvester Simplices
Sylvester simplices form a remarkable family of lattice simplices arising from the Sylvester sequence, with connections to number theory, convex geometry, and Ehrhart theory. In this talk, I will give an overview of these simplices, beginning with some historical context and the reasons why they have attracted attention in discrete geometry. I will then explain our motivation for studying them from the perspective of Ehrhart theory, focusing on questions related to lattice-point enumeration, unimodular triangulations, and the structure of their h^*-polynomials. This talk is based on joint work with Federico Castillo, Martina Juhnke and Germain Poullot.
03.06.2026 um 13:00 Uhr in 69/E23
Mieke Fink (Universität Osnabrück)
The polytope of all matroids
In this talk, I will introduce the valuative group of matroids, which allows to represent any matroid on the groundset $n$ of rank $r$ as a point in $\mathbb R ^{n \choose r}$. Ferroni and Fink initiated the study of the convex hull of all such points corresponding to matroids, which they call the 'polytope of all matroids'. I will explain this construction and present first result on the vertex edge graph of this polytope and certain special faces. I will also discuss linear projections to lower dimensional spaces.
09.06.2026 um 14:00 Uhr in 93/E02
Leonardo Saud Maria Leite (KTH Stockholm)
Totally nonnegative matrices and chain enumeration of r-cubical posets
Chain enumeration in partially ordered sets (posets) is a central topic in enumerative and algebraic combinatorics. The zeros of polynomials associated to chain enumeration have been studied frequently in the literature. Special attention has been given to the problem of determining if chain polynomials of posets are real-rooted for various classes of posets. For distributive lattices, this problem is equivalent to the Poset conjecture (Neggers-Stanley conjecture) for natural labelings, which was stated by Neggers (1978) in the seventies and disproved by Stembridge (2007). Brenti and Welker (2008) proved that the chain polynomials of the face lattices of simplicial polytopes are real-rooted, and conjectured that the same is true for any polytope. Athanasiadis (2007) proved Brenti and Welker’s conjecture for cubical polytopes. We prove that any lower unitriangular and totally nonnegative matrix gives rise to a family of polynomials with only real zeros. We use it to develop a general theory for chain enumeration in posets and zeros of chain polynomials. The results obtained extend and unify results of Brändén, Brenti, Welker and Athanasiadis. In the process we define a notion of h-vectors for r-cubical complexes and prove that the chain polynomial of shellable r-cubical complexes are real-rooted, thus extending Adin’s result on chain polynomials of shellable cubical complexes. This is a joint work with Petter Brändén.
10.06.2026 um 14:00 Uhr in 69/117
Dr. Oskar Henriksson (MPI - CBG)
The generic geometry of vertically parametrized systems
Polynomial systems that arise in applications are often sparse and parametric, with fixed monomial support and coefficients that depend on parameters. A central problem in applied algebraic geometry is to understand what the solution sets for such systems look like for generic parameter values. In the classical BKK framework, this is done under the assumption that all coefficients vary freely and independently. However, in many practical applications, there are algebraic dependencies between the coefficients, which makes the analysis more challenging. In this talk, I’ll discuss vertically parametrized systems, which arise in optimization and chemical reaction network theory, where there are linear dependencies between coefficients appearing in front of the same monomial. I will give an overview of recent results on the generic geometry of the solution sets of such systems through the lens of matroid theory, tropical geometry and toric geometry, with special focus on a recent tropical generalization of the BKK theorem to the vertical setting.
This is based on a series of joint works with Elisenda Feliu, Paul Helminck, Beatriz Pascual-Escudero, Yue Ren, Benjamin Schröter, and Máté Telek in various constellations.
17.06.2026 um 13:00 Uhr in 69/E23
Prof. Dr. Uwe Nagel (University of Kentucky)
TBA
23.06.2026 um 14:00 Uhr in 93/E02
Bogdan Ichim (Universität Bukarest)
TBA
01.07.2026 um 14:15 Uhr in 69/117
Prof. Dr. Eliza O`Reilly
Operatopes, Operanoids, and Noncommutative Zonoids
In this talk, we introduce and study the basic properties of a structured class of convex bodies calledoperatopes obtained by taking Minkowski sums of affine images of an operator norm ball. This notion generalizes that of zonotopes which are a special class of polytopes obtained by taking Minkowksi sums of line segments. In particular, operatopes include convex bodies that are non-polyhedral. Convex bodies obtained as limits of zonotopes are called zonoids, which can also be viewed as the expectation of a random line segment. Expanding on this interpretation, we can analogously define operanoids as the expectation of a random affine image of an operator norm ball. In studying the properties of operanoids when the dimension of the operator norm ball grows, we also arrive at a natural definition for a class of convex bodies called noncommutative zonoids, and we use the framework of free probability theory to illustrate basic properties and examples. We will discuss a selection of applications of zonoids in various domains and the analogous objects of interest for operanoids and noncommutative zonoids as well as open questions. This talk is based on joint work with Venkat Chandrasekaran.