Wintersemester 2025/2026

Stochastische Geometrie und räumliche Statistik

Vorträge:

_{28.10.     Dr. Ilya Gaiur – Institut des Hautes Études Scientifiques, Frankreich}

 

Title: Geometric Aspects of the Bessel Product Identities  
  

Abstract: Bessel functions and their various generalizations are classical objects in mathematical physics. Recently, formulas involving integrals of products of several Bessel functions have appeared in different physical contexts — such as the evaluation of certain types of Feynman integrals, mirror symmetry, and eigenvalue problems on hexagonal lattices (also known as fullerenes). All these formulas share a peculiar connection to the product formulas for Bessel functions, known as the Sonine–Gegenbauer formulas.     In my talk, I will review Sonine–Gegenbauer type formulas for classical Bessel functions and their higher analogues from the point of view of algebraic geometry. I will introduce the geometric structures and their periods that arise from these formulas using explicit approaches. If time allows, I will also discuss some integer sequences that emerge from these geometric objects.

The results I will present are based on joint work with Vladimir Rubtsov and Duco van Straten (arXiv:2405.03015).

 

Dienstag, 28. Oktober 2025, 16:00 Uhr, Helmholtzstr. 18, Raum 220

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_{30.10      Ass. Prof. Dr. Matthias Neumann - Institut für Statistik - Technische Universität Graz}
 

Title: Statistical analysis and stochastic 3D modeling of nanostructured electrode materials in sodium-ion batteries

Abstract: A data-driven modeling approach is presented to quantify the influence of morphology on effective properties of nanostructured sodium vanadium phosphate Na3V2 (PO4)3/ carbon com-posites (NVP/C), which are used as cathode material in sodium-ion batteries. This approach is based on the combination of advanced imaging techniques, experimental nanostructure characterization, and stochastic modeling of the 3D nanostructure consisting of NVP, carbon and pores. By 3D imaging and subsequent post-processing involving image segmentation, the spatial distribution of NVP is resolved in 3D, and the spatial distribution of carbon and pores is resolved in 2D. Based on this information, a parametric stochastic model, specifically a Pluri-Gaussian model, is calibrated to the 3D morphology of the nanostructured NVP/C particles. Model validation is performed by comparing the nanostructure of simulated NVP/C composites with image data in terms of morphological descriptors which have not been used for model calibration. Finally, the stochastic model is employed for predictive simulation to quantify the effect of varying the amount of carbon while keeping the amount of NVP constant. The presented methodology is combined with 3D imaging and electrochemically resolved transport simulations at the electrode scale for studying the impact of calendering on effective properties of NVP/C cathodes.
 

_{Donnerstag, 30. Oktober 2025, 15:00 Uhr, Helmholtzstr. 18, Raum 220}

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_{18.11.    Dr. Anton Klimovsky – Universität Würzburg}

  

Title: Markov chain hitting and meeting times via singular value decomposition
 
Abstract: We present a spectral framework for analyzing meeting and hitting times in (possibly non-reversible) Markov chains, based on the singular value decomposition (SVD) of suitable operators. This approach yields explicit formulas and sharp bounds for expected meeting and hitting times, and extends classical results beyond the reversible setting. For meeting times, we study the SVD of the diagonally killed generator of a pair of independent random walks. We show how rank-one approximations and matrix perturbation theory provide accurate estimates in dense random graphs, and we establish general conditions under which the expected meeting time scales linearly with the number of vertices. Applications include Erdős–Rényi graphs and stochastic block models, where we identify regimes with homogeneous and heterogeneous meeting time behavior. For hitting times, we derive a singular decomposition of the point-to-point expected hitting time using the SVD of the generator, applicable to non-reversible chains. We demonstrate the method on directed Erdős–Rényi graphs, obtaining asymptotically sharp results for average hitting times. Our framework opens up a range of spectral techniques for analyzing non-reversible Markov processes.

_{Dienstag, 18. November 2024, 16:00 Uhr, Helmholtzstr. 18, Raum 220}

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_{20.11.    Dr. Anna Goncharuk - V.N.Karazin Kharkiv National University}

_{Title: Implicit Linear difference equation over a non-Archimedean ring}

 

Abstract 

_{Donnerstag, 20. November, 2025, 14:00 Uhr, Helmholtzstr. 18, Raum 220}

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_{25.11.     Prof. Oleksandr Leonov und Prof. Liudmyla Poliakova - V.N.Karazin Kharkiv National University}

 

Title: Graph-based data analysis

Abstract: We present the concept of a metric graph as a framework for modeling complex data. In this representation, each data point is mapped to a node, and edges connect objects that are similar in some sense. This graph-based approach reveals hidden patterns in data and enables statistically meaningful conclusions. We illustrate the methodology through several applications, including understanding the spread of COVID-19 in the United States, detecting sub-populations in the Childhood Asthma Management Program, identifying systematic bias in clinical datasets, and other case studies.
 

_{Dienstag, 25. November, 2025, 16:00 Uhr, Helmholtzstr. 18, Raum 220}

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_{16.12.     Dr. Mikhail Chebunin - Universität Ulm}
 

Title: Uniqueness of the Infinite Cluster and Strong Sharpness of the Phase Transition in the Stationary Irreducible Marked Random Connection Model

Abstract: We study a random connection model (RCM) in a general spatial setting driven by a Poisson point process. We investigate the light-tailed behavior of connected components in the subcritical regime and establish that the stationary marked RCM, which includes the Boolean model with general compact grains and the so-called weighted RCM as special cases, admits at most one infinite cluster. Furthermore, under natural assumptions, we prove that this model exhibits the strong sharpness of the phase transition.

_{Dienstag, 16. Dezember, 2025, 16:00 Uhr, Helmholtzstr. 18, Raum 220}

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2026

_{08.01.    Richard Bölz - Universität Ulm}
 

Title: Enhancing weather radar data by removing non-meteorological echoes, using neural networks trained on synthetic weather data
 

Abstract: Meteorological weather radars are essential for atmospheric research and weather forecasting, but they often detect non-meteorological echoes from scatterers such as insects, birds, and ground clutter. These non-meteorological echoes can then lead to misinterpretations in quantitative precipitation estimation and hydrometeor classification, which cause difficulties for atmospheric research and weather forecasting. This talk introduces a novel AI-based approach to identify such non-meteorological echoes in polarimetric C-band Doppler radar data using a convolutional neural network. More specifically, we utilize a so-called U-net, which relies on large amounts of labeled radar data for training. To address the challenge of accurately labeling radar data consisting of meteorological and non-meteorological echoes, we generate synthetic training samples by combining preprocessed winter data (meteorological echoes) with cluttered summer data (non-meteorological echoes) provided by Deutscher Wetterdienst (DWD). These synthetic but realistic mixed training samples are further enhanced by data augmentation, such as scaling, rotation, and orientation inversion.  After training on synthetic data, the U-net is applied to operationally measured radar data and compared with hand-labeled ground truth. 
 

_{Donnerstag, 08. Januar 2026, 14:00 Uhr, Helmholtzstr. 18, Raum 220}

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_{13.01.     Dr. Alexander Van Werde -  Institut für Mathematische Stochastik / Universitäts Münster}
 

Title: On the spectral characterization of random graphs

Abstract: How much about a network can be deduced from the eigenvalues of associated matrices? Is the graph uniquely characterized by spectral information? Both positive and negative examples are known, but it remains poorly understood what happens in the typical case given by an Erdős-Rényi random graph.  In this talk, I will discuss what we believe to be true as well as results that support our conjectures. Time permitting, I will also discuss how the pursuit of rigorous results leads one to studying random Abelian groups that arise as cokernels of random matrices. 
 

_{Dienstag, 13. Januar, 2026, 16:00 Uhr, Helmholtzstr. 18, Raum 220}

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_{20.01.    Tom Kirstein - Universität Ulm}

_{Title: t.b.a}

_{Dienstag, 20. Januar, 2026, 16:00 Uhr, Helmholtzstr. 18, Raum 220}

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_{27.01.    Anina Dufter - Universität Ulm}
 

Title: Generative Adversarial Framework for Calibrating Excursion Set Models for the 3D Morphology in All-Solid-State Batery Cathodes

Abstract: A computational method for generating digital twins for the 3D morphology of three-phase microstructures (comprising active material, solid electrolyte, and pores) in all-solid-state battery (ASSB) cathodes is presented. Therefore, low-parametric stochastic geometry models are combined with generative adversarial networks (GANs) and calibrated using 2D scanning electron microscopy image data. Combining these two methods enables the exploitation of the interpretability and parameter control of low-parametric stochastic geometry models alongside the data-driven accuracy of GAN-generated structures, while reducing their respective restrictions— namely, the large number of uninterpretable parameters of GANs and the limited ability of stochastic geometry models to capture highly complex morphologies. This approach enables the generation of realistic 3D digital twins of material microstructures based solely on 2D image data of the 3D microstructure ensuring statistical consistency with experimental observations. Systematic variation of model parameters—revealing interpretable structural changes and enabling targeted exploration of structural scenarios beyond experimental observations—forms a foundation for digitally optimizing ASSB cathode materials by means of virtual materials testing through numerical simulations of effective properties and by deriving quantitative structure-property relationships.
 

_{Dienstag, 27. Januar, 2026, 16:00 Uhr, Helmholtzstr. 18, Raum 220}

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_{03.02.    Dr. Benedikt Prifling - Universität Ulm}
 

Title: Lattice Boltzmann simulations for computing the permeability of filter cakes

Abstract: Cake filtration is a separation process to split a suspension into a solid material and a liquid material. The 3D microstructure of the filter cake strongly influences the performance of the filter cake. One well-known effective macroscopic property of many porous media – among other filter cakes -  is the permeability, which can be measured experimentally but also obtained from 3D image data using methods from computational fluid dynamics (CFD). In case of filter cakes, permeability – roughly speaking – quantifies the average flow velocity relative to the applied pressure gradient and is a key characteristic that is strongly related to the performance of the filter cake. One popular choice for a numerical CFD framework is the lattice Boltzmann method that (among others) allows to simulate flow through a porous medium. In the present talk, the core concepts and equations behind the lattice Boltzmann method are explained, including various experimentally determined parameters that are required to successfully implement flow simulations for filter cakes via the lattice Boltzmann method. This framework can then be used to investigate quantitative structure-property relationships for filter cakes based on virtual, but realistic structures that are generated via data-driven stochastic 3D microstructure modeling. 

_{Dienstag, 03. Februar, 2026, 16:00 Uhr, Helmholtzstr. 18, Raum 220}

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_{10.02.    Ass. Prof. Dr. Orkun Furat - University of Southern Denmark, Odense}
 

Title: Physics-informed surrogate models for computing 3D electromagnetic fields transformed by metasurfaces
 

Abstract: Metasurfaces are nanostructured materials which are, in optical applications, often realized as arrays of nanopillars with varying shapes and sizes. The morphology of these metasurfaces allow for the manipulation of electromagnetic (EM) waves, but their design typically requires performing a large number of numerical simulations of EM waves, i.e., repeatedly solving Maxwell’s equations numerically on candidate metasurface geometries. These approaches can become computationally prohibitive for large metasurface domains or when the number of parameters describing the nanopillar shapes, sizes, and arrangements is large. Recent advances have demonstrated that physics-informed neural networks (PINNs) can serve as surrogate models for approximating solutions to Maxwell’s equations for metasurfaces. Such surrogate models offer several advantages: they are differentiable, significantly faster than conventional solvers and can be embedded directly into numerical optimization loops, e.g., for inverse-design of metasurfaces. In this work, we deploy PINNs to train surrogate models that can predict 3D EM fields transformed by metasurfaces. We generate synthetic training data consisting of 3D metasurface geometries together with their corresponding 3D EM fields obtained by numerically solving Maxwell’s equations. Using the synthetic data, we train PINNs that incorporate residuals capturing deviations from Maxwell’s equations, to minimize physical inconsistencies of predicted 3D EM fields. Once trained, our surrogate model rapidly predicts 3D EM fields for previously unseen metasurface geometries and enables efficient gradient-based design of nanostructured materials for EM wave control.
 

The presented results are based on joint work with Vinay C. Gogineni, Henrik Bindslev and Esmaeil S. Nadimi.

_{Dienstag, 10. Februar, 2026, 16:00 Uhr, Helmholtzstr. 18, Raum 220}

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<sub>17.02.    Prof. Dr. Serguei Dachian – Lille University - Frankreich

Title: t.b.a</sub>

_{Dienstag, 17. Februar, 2026, 16:00 Uhr, Helmholtzstr. 18, Raum 220}

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_Gäste:

• Prof. Dr. Serguei Dachian – Lille University - Frankreich

• Dr. Ilya Gaiur – Institut des Hautes Études Scientifiques, Frankreich

• Ass. Prof. Dr. Matthias Neumann - Institut für Statistik -  Technische Universität Graz

• Dr. Anton Klimovsky – Universität Würzburg

• Dr. Anna Goncharuk - V.N.Karazin Kharkiv National University

• Prof. Oleksandr Leonov und Prof. Liudmyla Poliakova - V.N.Karazin Kharkiv National University

• Dr. Alexander Van Werde -  Institut für Mathematische Stochastik / Universitäts Münster

• Ass. Prof. Dr. Orkun Furat - University of Southern Denmark, Odense

• Prof. Dr. Serguei Dachian – Lille University - Frankreich