Mathematisches Forschungskolloquium 2026
Das Forschungskolloquium betrachtet mathematische Themen tiefergreifend und differenziert. So soll ein Austausch über die mathematischen Spezialisierungen der verschiedenen Arbeitsgruppen am Institut und darüber hinaus gefördert werden. Außerdem sollen auch Studierende (hauptsächlich Master-Studierende) durch das Seminar die Gelegenheit erhalten, sich über spezifische Aspekte mathematischer Themen zu informieren.
Forschungskolloquium mit Herrn Hector Vargas Alvarez (TU Chalmers, Göteborg)
"Data-driven modelling, analysis and control of crowd dynamics"
Abstract: Complex systems such as pedestrian crowds exhibit collective behaviours that emerge from nonlinear interactions among many individuals. Modeling these systems across scales remains a fundamental challenge, particularly when deriving macroscopic governing equations from microscopic agent-based models is impractical. This work presents a scientific machine learning framework for learning macroscopic crowd dynamics directly from microscopic simulations inspired by equation-free computations. The proposed approach combines coarse-graining, manifold learning, and reduced-order modeling to construct a low-dimensional representation of the macroscopic state while preserving key physical properties, including mass conservation. Evolution operators are then learned directly in this reduced space, enabling efficient long-horizon prediction of crowd dynamics without explicitly specifying continuum equations. The learned operators provide a unified macroscopic representation that naturally supports higher-level tasks such as state estimation and control. Building on this representation, Physics-Informed Neural Networks are employed to design observers and controllers that enforce physical consistency. The observer framework is first validated on benchmark dynamical systems and subsequently applied to the learned crowd models, demonstrating accurate reconstruction of macroscopic states from partial observations. A control-oriented extension is also developed and validated on benchmark systems.
Donnerstag, 09.07.2026, 13:15 Uhr, Ulmenstr. 69, Haus 3, R 427
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Seminarleiter: Prof. Jens Starke
Forschungskolloquium mit Frau Dr. Mahdieh Ebrahimi (IPKM, TU Darmstadt)
"The Impact of Noise on the Nonlinear Schrödinger Equation"
Abstract: This talk explores how noise affects the discrete nonlinear Schrödinger equation (DNSE), a fundamental model in nonlinear physics with applications in condensed matter and optics. The focus is on how stochastic perturbations influence both the dynamics and thermodynamics of the system, particularly the formation and stability of localized excitations (breathers) and the transition between localized and disordered phases. After briefly reviewing the DNSE and its key properties, a stochastic extension (SDNSE) is introduced by coupling the system to a heat bath, allowing for a consistent description of equilibrium states, including regimes with negative temperature. To investigate the phase diagram of the model, a structure-preserving numerical method is developed to enable stable long-term simulations. The results show that noise significantly impacts how the system relaxes and transitions between phases. In particular, the transition between disordered and localized states is identified as first order, with a finite critical temperature, and metastable energy states can be understood through a simple mean-field picture. Overall, the findings highlight that stochastic effects play a central role in both the pathway to equilibrium and the stability of localized structures.
Mittwoch, 08.07.2026, 15:15 Uhr, Ulmenstr. 69, Haus 3, HS 326/327
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Seminarleiter: Dr. Wolfram Just
Forschungskolloquium mit Herrn Dr. Christian Kaspers (IAG, OVGU Magdeburg)
"kth-order sum-free functions and nonvanishing k-flats"
Abstract
Mittwoch, 01.07.2026, 15:00 Uhr, Ulmenstr. 69, Haus 3, SR 228
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Seminarleiterin: Prof. Dr. Gohar Kyureghyan
Forschungskolloquium mit Herrn Prof. Nicolas Ginoux (Université de Lorraine)
"Eigenvalues of the magnetic Dirac operator on closed Riemannian spin manifolds"
Abstract: The magnetic Dirac operator is a first-order linear differential operator involving the standard spin Dirac operator and a magnetic potential.
In this talk, we concentrate on its spectrum and in particular on the interactions between the smallest eigenvalues and the geometry of the underlying Riemannian manifold.
This is a joint work with Volker Branding (Universität Rostock) and Georges Habib (Lebanese University), see https://arxiv.org/abs/2512.13338
Mittwoch, 01.07.2026, 15:00 Uhr, Ulmenstr. 69, Haus 3, HS 326/327
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Seminarleiter: Prof. Dr. Volker Branding
Forschungskolloquium mit Herrn Dr. Oskar Riedler (Universität Potsdam)
"Scalar-rigid submersions are Riemannian products"
Abstract: Scalar curvature is a very weak and flexible local invariant in Riemannian geometry. So it is surprising that coupling lower scalar curvature bounds with seemingly harmless topological conditions can recover very powerful rigidity statements, such as Llarull’s theorem or the positive mass theorem.
In this talk I will begin by introducing some aspects related to the comparison geometry of lower scalar curvature bounds, focussing in particular on Llarull’s theorem. After this I will discuss a recent rigidity theorem in this setting. This is joint work with Thomas Tony.
Donnerstag, 18.06.2026, 17:00 Uhr, Ulmenstr. 69, Haus 3, HS 326/327
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Seminarleiter: Prof. Dr. Volker Branding
Forschungskolloquium mit Frau Dr. Simona Nistor Barna ("Alexandru Ioan Cuza" University of Iasi, Romania)
"Stability for Energy-Type Functionals"
Abstract: Conformal-biharmonic maps arise as critical points of the conformal-bienergy functional, a second-order functional obtained by modifying the bienergy functional through curvature terms motivated by conformal geometry. In dimension four, this functional is conformally invariant, which makes it particularly relevant in variational problems in conformal geometry.
In this talk, I will focus on stability properties of conformal-biharmonic maps. In particular, I will discuss the conformal-biharmonic stability of the identity map on compact Einstein manifolds with non-negative scalar curvature, and show that its conformal-biharmonic index coincides with the classical harmonic index, with a notable exception in the case of the four-dimensional sphere. We will also present results on hypersurfaces in space forms, including computations of the index and nullity of great hyperspheres.
Mittwoch, 10.06.2026, 16:00 Uhr, Ulmenstr. 69, Haus 3, HS 326/327
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Seminarleiter: Prof. Dr. Volker Branding
Forschungskolloquium mit Herrn Prof. Dr. Stefan Hoderlein (Emory University, Atlanta USA)
"Moment estimation in a correlated random coefficients linear panel data model: a functional fixed point approach to identification and estimation"
Abstract: We develop a linear regression panel data model allowing random coefficients to be correlated with regressors not only within periods but also across periods. The random coefficients are modeled as sums of independent possibly nonidentically distributed past and current shocks. This structure allows feedback, in the sense that future regressors can be correlated with all past shocks, and also allows all lagged dependent variables to be regressors. For each time period, we identify all marginal first moments of the random coefficients. These moments have causal interpretations. The identification results rest on a novel functional fixed point argument and lead to natural estimators of these moments. We provide simulation evidence of the usefulness of this approach.
Mittwoch, 10.06.2026, 16:00 Uhr, Ulmenstr. 69, Haus 3, HS 125
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Seminarleiter: Prof. Dr. Alexander Meister
Forschungskolloquium mit Frau Kerrin Bielser (Europa-Universität Flensburg)
"Über eine Frage von Katona zu Familien von Paaren -- Ein kleines Problem aus der extremalen Kombinatorik"
Zusammenfassung: Klassischerweise wird in der extremalen Mengentheorie untersucht, wie groß ein Mengensystem unter gewissen Bedingungen höchstens sein kann. In diesem Vortrag werden wir uns nach einer kurzen Einführung mit Familien befassen, welche eng mit Semi-Antiketten verwandt sind. Bei verschiedenen Lösungsansätzen und Beweisen kommen sowohl elementare Operationen an Ketten als auch die Sperner-Eigenschaft gewisser Posets zum Einsatz. Dabei zeigt sich ein enger Zusammenhang zu Fragestellungen aus mathematischen Untersuchungen zu Datenbanken.
Die vorgestellten Ergebnisse basieren auf gemeinsamer Arbeit mit Gyula O.H. Katona.
Mittwoch, 03.06.2026, 15:00 Uhr, Ulmenstr. 69, Haus 3, SR 228
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Seminarleiter: Prof. Dr. Thomas Kalinowski
Forschungskolloquium mit Herrn Dr. Johannes Schmalz (Universität des Saarlandes)
"Bridging Automated Planning and Spectral Graph Theory"
Abstract: Automated planning concerns itself with combinatorial optimisation problems where an agent must navigate a state-space using a discrete set of actions -- a famous toy problem is to stack blocks on a table into a specific arrangement, only being allowed to lift one at a time. These problems are closely related to the shortest path problems on graphs. On the other hand, spectral graph theory considers different matrix representations of graphs, and studies what information can be read from their eigenvectors and eigenvalues, with applications to many areas of computer science, but surprisingly few relevant to automated planning. This talk will discuss an existing path-finding algorithm from spectral graph theory and its connections to automated planning, as a step in bridging the two disciplines.
Donnerstag, 28.05.2026, 13:00 Uhr, Ulmenstr. 69, Haus 3, SR 228
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Seminarleiter: Prof. Dr. Thomas Kalinowski
Forschungsseminar mit Herrn Lukas Klawuhn (AG Algebra, Universität Paderborn)
"Why I love association schemes - an introduction to Delsarte theory"
Abstract: Interesting combinatorial structures can often be characterised as special subsets of association schemes. In his PhD thesis, Philippe Delsarte developed powerful linear programming techniques to prove non-existence and uniqueness results for such structures. In particular, this applies to error-correcting codes. Ideas of this type were fundamental in the work for which Maryna Viazovska was awarded the Fields medal in 2022. This talk will begin with an overview of Delsarte theory.
We will use this theory to study perfect matchings. We show that 1-factorisations of the complete graph are special subsets in the sense of Delsarte. The same is true for hyperfactorisations and other generalisations of 1-factorisations. The characterisation of these structures as a special subset of an association scheme gives rise to divisibility conditions and non-existence results. We also give a construction of hyperfactorisations using finite geometry.
No particular knowledge of association schemes will be required to appreciate this talk.
Mittwoch, 22.04.2026, 15:00 Uhr, Ulmenstr. 69, Haus 3, SR 228
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Seminarleiter: Prof. Dr. Thomas Kalinowski