@unpublished{65232,
abstract = {{On finite regular graphs, we construct Patterson-Sullivan distributions associated with eigenfunctions of the discrete Laplace operator via their boundary values on the phase space. These distributions are closely related to Wigner distributions defined via a pseudo-differential calculus on graphs, which appear naturally in the study of quantum chaos. Using a pairing formula, we prove that Patterson-Sullivan distributions are also related to invariant Ruelle distributions arising from the transfer operator of the geodesic flow on the shift space. Both relationships provide discrete analogues of results for compact hyperbolic surfaces obtained by Anantharaman-Zelditch and by Guillarmou-Hilgert-Weich.}},
author = {{Arends, Christian and Palmirotta, Guendalina}},
booktitle = {{arXiv:2603.09779}},
pages = {{38}},
title = {{{Patterson-Sullivan distributions of finite regular graphs}}},
year = {{2026}},
}
@proceedings{64797,
editor = {{Birk, Lisa and Loth, Gerrit and Jotzo, Luca and Binder, Karin and Frischemeier, Daniel}},
location = {{Münster}},
publisher = {{International Association for Statistics Education}},
title = {{{14th IASE Satellite Conference "Statistics and Data Science Education in STEAM"}}},
doi = {{10.52041/iase25.158}},
year = {{2026}},
}
@article{63135,
abstract = {{We propose a definition of Coxeter-Dynkin algebras of canonical type generalising the definition as a path algebra of a quiver. Moreover, we construct two tilting objects over the squid algebra - one via generalised APR-tilting and one via one-point-extensions and reflection functors - and identify their endomorphism algebras with the Coxeter-Dynkin algebra. This shows that our definition gives another representative in the derived equivalence class of the squid algebra, and hence of the corresponding canonical algebra. Finally, we have a closer look at the Grothendieck group and the Euler form which illustrates the connection to Saito's classification of marked extended affine root systems. On the other hand, this enables us to prove that in the domestic case Coxeter-Dynkin algebras are of finite representation type.}},
author = {{Perniok, Daniel}},
journal = {{Journal of Pure and Applied Algebra}},
number = {{5}},
title = {{{Coxeter-Dynkin algebras of canonical type}}},
doi = {{10.1016/j.jpaa.2026.108250}},
volume = {{230}},
year = {{2026}},
}
@article{65512,
abstract = {{Zusammenfassung
Risikokompetenz beinhaltet auch die Fähigkeit, stochastische Informationen, wie beispielsweise Anteile und Wahrscheinlichkeiten, richtig zu versprachlichen. Aus der Forschung zu bedingten Wahrscheinlichkeiten und Bayesianischen Aufgaben ist bekannt, dass die Nutzung von Visualisierungen und sogenannten „natürlichen Häufigkeiten“ (z. B. „80 von 100 Personen“) statt Wahrscheinlichkeiten in Prozent Verwechslungen beim Bestimmen von Wahrscheinlichkeiten eindämmen kann. Über den umgekehrten Prozess – das Versprachlichen von in Visualisierungen dargestellten Informationen – ist bisher jedoch wenig bekannt, obwohl diese Versprachlichungen auch für den Aufbau konzeptuellen Wissen als essentiell angesehen werden. In der vorliegenden Studie wurde daher untersucht, wie gut Schüler:innen die Versprachlichung von in Visualisierungen dargestellten Anteilen und natürlichen Häufigkeiten gelingt. Dazu wurde mit 138 Realschüler:innen aus der 9. Jahrgangsstufe ein Papier-und-Bleistift-Test durchgeführt, bei dem den Teilnehmenden nacheinander je ein (vollständig ausgefülltes) Baumdiagramm und ein Netzdiagramm präsentiert wurde. Die Schüler:innen sollten die inhaltliche Bedeutung der in der Visualisierung dargestellten stochastischen Informationen möglichst genau versprachlichen. Fokus der Studie ist der Einfluss der Visualisierung (Baumdiagramm vs. Netzdiagramm) und des Informationsformats der Visualisierung (Anteile in Prozent vs. natürliche Häufigkeiten) auf die richtige Versprachlichung von verschiedenen Relationstypen (Schnittinformationen vs. bedingte Informationen). Die Ergebnisse zeigen unter anderem, dass Informationen in natürlichen Häufigkeiten deutlich besser versprachlicht werden als in Prozenten und dass Schnittinformationen in Prozent besser anhand von Netzdiagrammen als von Baumdiagrammen versprachlicht werden. Die gewonnenen Erkenntnisse geben überdies Einblicke in typische (fehlerhafte) Versprachlichungen von Schüler:innen und könnten als Basis für die Entwicklung eines sprachsensiblen Unterrichts zu Anteilen und Wahrscheinlichkeiten im schulischen Stochastikunterricht dienen.}},
author = {{Rößner, Michael and Binder, Karin and Albrecht, Julian}},
issn = {{0173-5322}},
journal = {{Journal für Mathematik-Didaktik}},
number = {{1}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Versprachlichung von Anteilen und natürlichen Häufigkeiten anhand von Baum- und Netzdiagrammen Verbalization of proportions and natural frequencies based on tree diagrams and net diagrams}}},
doi = {{10.1007/s13138-026-00267-1}},
volume = {{47}},
year = {{2026}},
}
@article{61759,
abstract = {{Intersection distribution and non-hitting index are concepts introduced recently by Li and Pott as a new way to view the behaviour of a collection of finite field polynomials. With both an algebraic interpretation via the intersection of a polynomial with a set of lines, and a geometric interpretation via a (q+1)-set possessing an internal nucleus, the concepts have proved their usefulness as a new way to view various long-standing problems, and have applications in areas such as Kakeya sets. In this paper, by exploiting connections with diverse areas including the theory of algebraic curves, cyclotomy and the enumeration of irreducible polynomials, we establish new results and resolve various Open Problems of Li and Pott. We prove geometric results which shed new light on the relationship between intersection distribution and projective equivalence of polynomials, and algebraic results which describe and characterise the degree of Sf - the index of the largest non-zero entry in the intersection distribution of f. We provide new insights into the non-hitting spectrum, and show the limitations of the non-hitting index as a tool for characterisation. Finally, the benefits provided by the connections to other areas are evidenced in two short new proofs of the cubic case. }},
author = {{Klawuhn, Lukas-André Dominik and Huczynska, Sophie and Paterson, Maura}},
journal = {{Finite Fields and Their Applications}},
publisher = {{Elsevier}},
title = {{{The Intersection Distribution: New Results and Perspectives}}},
doi = {{10.1016/j.ffa.2026.102828}},
volume = {{114}},
year = {{2026}},
}
@article{65631,
abstract = {{Abstract
Mathematics textbooks used to be the key resource for students’ self-regulated learning of mathematics. Primarily due to the digitalization of society, students have potentially greater access to a wider range of resources such as internet search engines, learning platforms, educational videos, and Generative AI. This study investigates the role of the mathematics textbook in comparison to other resources within students’ self-regulated learning practices. Data were collected via a survey of 1101 German secondary students, representing three school types (
Gymnasium
,
Gesamtschule
,
Realschule
) and three grade levels (6, 9, and upper secondary). The questionnaire assessed the frequency of resource use in and outside class, reasons and purposes of use, and resource-based strategies when facing learning challenges outside class. Results show that the printed mathematics textbook is the most frequently used resource both in class and outside class. The textbook remains the most relevant resource for key purposes, such as an aid for doing homework and preparing for tests and exams. However, its dominance diminishes with age: in upper secondary school, students increasingly rely on self-created notes, and online resources. Correlation analyses reveal moderate to strong links between in-class and out-of-class use, suggesting an association between resource use and classroom culture. The findings underscore the textbook’s enduring centrality as a foundational, trusted resource within a dynamic and increasingly diverse learning environment. This study calls for pedagogical approaches that integrate textbooks more intentionally within broader resource systems, supporting students’ agency and strategic resource selection in an era of digital abundance.
}},
author = {{Stallmeister, Lea and Rezat, Sebastian}},
issn = {{0013-1954}},
journal = {{Educational Studies in Mathematics}},
keywords = {{mathematics, textbooks, userstudy, resources, digital resources, students, secondary eduction}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{The role of the mathematics textbook in times of resource diversity}}},
doi = {{10.1007/s10649-026-10511-7}},
year = {{2026}},
}
@article{65630,
abstract = {{Mathematics textbooks used to be the key resource for students’ self-regulated learning of mathematics. Primarily due to the digitalization of society, students have potentially greater access to a wider range of resources such as internet search engines, learning platforms, educational videos, and Generative AI. This study investigates the role of the mathematics textbook in comparison to other resources within students’ self-regulated learning practices. Data were collected via a survey of 1101 German secondary students, representing three school types (Gymnasium, Gesamtschule, Realschule) and three grade levels (6, 9, and upper secondary). The questionnaire assessed the frequency of resource use in and outside class, reasons and purposes of use, and resource-based strategies when facing learning challenges outside class. Results show that the printed mathematics textbook is the most frequently used resource both in class and outside class. The textbook remains the most relevant resource for key purposes, such as an aid for doing homework and preparing for tests and exams. However, its dominance diminishes with age: in upper secondary school, students increasingly rely on self-created notes, and online resources. Correlation analyses reveal moderate to strong links between in-class and out-of-class use, suggesting an association between resource use and classroom culture. The findings underscore the textbook’s enduring centrality as a foundational, trusted resource within a dynamic and increasingly diverse learning environment. This study calls for pedagogical approaches that integrate textbooks more intentionally within broader resource systems, supporting students’ agency and strategic resource selection in an era of digital abundance.}},
author = {{Stallmeister, Lea and Rezat, Sebastian}},
journal = {{Educational Studies in Mathematics}},
publisher = {{Springer}},
title = {{{The role of the mathematics textbook in times of resource diversity}}},
doi = {{10.1007/s10649-026-10511-7}},
year = {{2026}},
}
@article{65645,
abstract = {{Curriculum material is often designed to address content-specific intended learning goals. However, research indicates that teachers’ personal goals may cause misalignments between their implementation of curriculum material and its intended learning goals. This study aims to investigate misalignments between teachers’ implementation of curriculum material and its intended learning goals and to which extent they are caused by teachers’ personal goals. To reach this aim, a qualitative study was conducted to examine how eight vocational school teachers implemented the learning activity “How many?” suggested for the initial training of early childhood educators on the topic of set perception and determination of cardinality. Each participant provided a lesson plan and self-recorded lesson video on the topic of set perception and determination of cardinality. In addition, participants were interviewed on how they used the provided curriculum material for designing their lessons and their potential reasons to adapt or omit “How many?”. To evaluate their lesson design’s alignment with the activity’s intended learning goals, the participants' lesson plans were analyzed using qualitative content analysis. Triangulation of the findings with the interview data revealed that only one participant fully adopted the intended learning goals as her own and implemented the activity completely in line with its intended learning goals. Meanwhile, the remaining participants’ personal goals, such as reducing math anxiety, seemed to cause misalignments regarding the intended learning goals. The study's results detail further constraints and affordances to the alignment between teachers’ lesson designs and learning goals intended by curriculum material. It is followed that it is central to support teachers in adopting intended learning goals as their personal goals. Otherwise, teachers’ classroom implementation of curriculum material may not suffice to reach desired outcomes.}},
author = {{Richter, Alix and Bruns, Julia}},
issn = {{1306-3030}},
journal = {{International Electronic Journal of Mathematics Education}},
number = {{2}},
publisher = {{Modestum Ltd}},
title = {{{All a question of the goal? Re-tracing (mis)alignments between teachers’ implementations of curriculum material and intended learning goals in the context of early childhood educator training in Germany}}},
doi = {{10.29333/iejme/18564}},
volume = {{21}},
year = {{2026}},
}
@inproceedings{64211,
author = {{Wiebe, Vivien and Häsel-Weide, Uta}},
booktitle = {{Proceedings of the Nineteenth ERME Topic Conference: Connecting the Learning of Mathematics Teaching to Practice}},
editor = {{Mosvold, R. and Fauskanger, J. and Ferretti, F. and Vondrová, N.}},
location = {{Prag}},
pages = {{122--129}},
title = {{{ Initiating and establishing mathematical practices of determining and transforming numbers as a foundational skill in fostering mathematics teaching}}},
year = {{2026}},
}
@article{65745,
abstract = {{Abstract
In this work, we address the numerical identification of entanglement in dynamical scenarios. To this end, we consider different programs based on the restriction of the evolution to the set of separable (i.e., non-entangled) states, together with the discretization of the space of variables for numerical computations. As a first approach, we apply linear splitting methods to the restricted, continuous equations of motion derived from variational principles. We utilize an exchange interaction Hamiltonian to confirm that the numerical and analytical solutions coincide in the limit of small time steps. The application to different Hamiltonians shows the wide applicability of the method to detect dynamical entanglement. To avoid the derivation of analytical solutions for complex dynamics, we consider variational, numerical integration schemes, introducing a variational discretization for Lagrangians linear in velocities. Here, we examine and compare two approaches: one in which the system is discretized before the restriction is applied, and another in which the restriction precedes the discretization. We find that the "first-discretize-then-restrict" method becomes numerically unstable, already for the example of an exchange-interaction Hamiltonian, which can be an important consideration for the numerical analysis of constrained quantum dynamics. Thereby, broadly applicable numerical tools, including their limitations, for studying entanglement over time are established for assessing the entangling power of processes that are used in quantum information theory.}},
author = {{Offen, Christian and Wembe, Boris and Ares, Laura and Sperling, Jan and Ober-Blöbaum, Sina}},
issn = {{1751-8113}},
journal = {{Journal of Physics A: Mathematical and Theoretical}},
publisher = {{IOP Publishing}},
title = {{{Numerical approaches to entangling dynamics from variational principles}}},
doi = {{10.1088/1751-8121/ae6d51}},
year = {{2026}},
}
@article{65742,
abstract = {{Abstract
In this work, we address the numerical identification of entanglement in dynamical scenarios. To this end, we consider different programs based on the restriction of the evolution to the set of separable (i.e., non-entangled) states, together with the discretization of the space of variables for numerical computations. As a first approach, we apply linear splitting methods to the restricted, continuous equations of motion derived from variational principles. We utilize an exchange interaction Hamiltonian to confirm that the numerical and analytical solutions coincide in the limit of small time steps. The application to different Hamiltonians shows the wide applicability of the method to detect dynamical entanglement. To avoid the derivation of analytical solutions for complex dynamics, we consider variational, numerical integration schemes, introducing a variational discretization for Lagrangians linear in velocities. Here, we examine and compare two approaches: one in which the system is discretized before the restriction is applied, and another in which the restriction precedes the discretization. We find that the "first-discretize-then-restrict" method becomes numerically unstable, already for the example of an exchange-interaction Hamiltonian, which can be an important consideration for the numerical analysis of constrained quantum dynamics. Thereby, broadly applicable numerical tools, including their limitations, for studying entanglement over time are established for assessing the entangling power of processes that are used in quantum information theory.}},
author = {{Offen, Christian and Wembe, Boris and Ares, Laura and Sperling, Jan and Ober-Blöbaum, Sina}},
issn = {{1751-8113}},
journal = {{Journal of Physics A: Mathematical and Theoretical}},
publisher = {{IOP Publishing}},
title = {{{Numerical approaches to entangling dynamics from variational principles}}},
doi = {{10.1088/1751-8121/ae6d51}},
year = {{2026}},
}
@inproceedings{65746,
abstract = {{This paper presents a class of structure-preserving numerical methods for quantum optimal control problems, based on commutator-free Cayley integrators. Starting from the Krotov framework, we reformulate the forward and backward propagation steps using Cayley-type schemes that preserve unitarity and symmetry at the discrete level. This approach eliminates the need for matrix exponentials and commutators, leading to significant computational savings while maintaining higher-order accuracy. We first recall the standard linear setting and then extend the formulation to nonlinear Schrödinger and Gross-Pitaevskii equations using a Cayley-polynomial interpolation strategy. Numerical experiments on state-transfer problems illustrate that the CF-Cayley method achieves the same accuracy as high-order exponential or Cayley-Magnus schemes at substantially lower cost, especially for longtime or highly oscillatory dynamics. In the nonlinear regime, the structure-preserving properties of the method ensure stability and norm conservation, making it a robust tool for large-scale quantum control simulations. The proposed framework thus bridges geometric integration and optimal control, offering an efficient and reliable alternative to existing exponential-based propagators.}},
author = {{Wembe Moafo, Boris Edgar and Ali, Usman and Meier, Torsten and Ober-Blöbaum, Sina}},
location = {{Reykjavík, Iceland}},
title = {{{Cayley Commutator-free Methods for Krotov-Type Algorithms in Quantum Optimal Control}}},
doi = {{10.48550/ARXIV.2603.11697}},
year = {{2026}},
}
@unpublished{65744,
abstract = {{Optimal control problems with symmetries often admit a non stationary turnpike property called trim turnpike, which characterizes the convergence of optimal solutions to certain symmetry induced trajectories called trim primitives. In this paper we establish an exponential trim turnpike property for a class of optimal control problems with structural properties related to Abelian Lie group symmetries. The key ingredient of our approach is the introduction of an appropriate reduced optimal control problem. We show that extremals of the original problem can be characterized through a reduced Hamiltonian boundary value problem that coincides with the optimality system of the reduced problem. Under a hyperbolicity assumption on the equilibrium of the corresponding reduced Hamiltonian system we prove that optimal trajectories remain exponentially close, up to boundary layers near the endpoints, to a trim primitive defined by the static reduced problem. The theoretical results are illustrated on three representative examples: linear and nonlinear problems with quadratic cost and the Kepler orbital transfer problem.}},
author = {{Maslovskaya, Sofya and Ober-Blöbaum, Sina and Wembe Moafo, Boris Edgar}},
title = {{{Non static exponential turnpike property for optimal control problems with symmetries and boundary conditions}}},
year = {{2026}},
}
@article{65747,
abstract = {{In this work, we address the numerical identification of entanglement in dynamical scenarios. To this end, we consider different programs based on the restriction of the evolution to the set of separable (i.e., non-entangled) states, together with the discretization of the space of variables for numerical computations. As a first approach, we apply linear splitting methods to the restricted, continuous equations of motion derived from variational principles. We utilize an exchange interaction Hamiltonian to confirm that the numerical and analytical solutions coincide in the limit of small time steps. The application to different Hamiltonians shows the wide applicability of the method to detect dynamical entanglement. To avoid the derivation of analytical solutions for complex dynamics, we consider variational, numerical integration schemes, introducing a variational discretization for Lagrangians linear in velocities. Here, we examine and compare two approaches: one in which the system is discretized before the restriction is applied, and another in which the restriction precedes the discretization. We find that the "first-discretize-then-restrict" method becomes numerically unstable, already for the example of an exchange-interaction Hamiltonian, which can be an important consideration for the numerical analysis of constrained quantum dynamics. Thereby, broadly applicable numerical tools, including their limitations, for studying entanglement over time are established for assessing the entangling power of processes that are used in quantum information theory.}},
author = {{Offen, Christian and Wembe, Boris and Ares, Laura and Sperling, Jan and Ober-Blöbaum, Sina}},
issn = {{1751-8113}},
journal = {{Journal of Physics A: Mathematical and Theoretical}},
publisher = {{IOP Publishing}},
title = {{{Numerical approaches to entangling dynamics from variational principles}}},
doi = {{10.1088/1751-8121/ae6d51}},
year = {{2026}},
}
@article{65865,
abstract = {{Mathematical problem solving is a highly complex competence that needs
to be supported throughout the learning process. This study examines the role of
problem-solving heuristics among 73 sixth-grade students in a German secondary
school (Gesamtschule). Specifically, we focus on the empirical relationship between
the occurrence of heuristics, their suitability, and application, as well as their contribution
to problem-solving success. To this end, we developed a heuristic training that
introduced strategy keys (heuristic aid cards) accompanied by explanatory videos. By
leveraging variations in the successful application of the heuristics between students
and across multiple sessions (73 students in 4 training situations and 3 problems
in a final test), we discover from regression models with student and task-fixed effects
that a successful use of heuristics (i.e., an heuristic occurred, that heuristic had
a high suitability regarding the problem, and it was applied correctly) leads to more
successful mathematical problem solving. Regarding the underlying mechanism, we
find that all dimensions of heuristic use (occurrence, suitability, and application
of heuristics) are positively related to problem-solving success. When comparing
the predictive capacity of all three aspects, we identified the correct application of
heuristics as particularly conducive for better problem-solving success. In comparing
the group of students with high to those with low initial math competence, we find no significant differences in the relationship between heuristic use and problemsolving
success across achievement groups. Our results emphasize the crucial role
of heuristic application in mathematical problem solving, which generally benefits
students regardless of their overall math competence.}},
author = {{Herold-Blasius, Raja and Kleinschmidt, Hannah and Ziller, Conrad}},
journal = {{Journal für Mathematik-Didaktik}},
number = {{6}},
title = {{{Dimensions of Heuristic Use in Mathematical Problem Solving: Evidence from Early Secondary School Students}}},
doi = {{https://doi.org/10.1007/s13138-026-00270-6}},
volume = {{47}},
year = {{2026}},
}
@unpublished{65916,
author = {{Jakob, Johanna}},
title = {{{Diffeomorphism groups of compact locally polyhedral manifolds}}},
year = {{2026}},
}
@article{66060,
author = {{Claes, Leander and Winkler, Michael}},
issn = {{1420-9004}},
journal = {{Nonlinear Differential Equations and Applications NoDEA}},
number = {{4}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Local strong solutions in a quasilinear Moore-Gibson-Thompson type model for thermoviscoelastic evolution in a standard linear solid}}},
doi = {{10.1007/s00030-026-01239-7}},
volume = {{33}},
year = {{2026}},
}
@article{66057,
author = {{Bullerjahn, Nils and Kovács, Balázs}},
journal = {{ArXiv}},
title = {{{Error estimates for $A$-stable backward difference full discretizations of Willmore flow of closed surfaces}}},
doi = {{10.48550/arXiv.2606.25934}},
year = {{2026}},
}
@article{66074,
abstract = {{Abstract
This study investigates how secondary students construct and evaluate decision trees in an open exploratory task using CODAP. By analyzing students’ tree products and oral self-reports, we identified different data-based and context-based approaches to predictor selection and stopping criteria. Students engaged with key ideas of predictive modeling, including classification, model construction, accuracy, generalization, and interpretability. Informal exploration offered rich opportunities for subsequent teaching by enabling students to begin reconstructing central technical ideas and critical tensions of predictive modeling through diverse but meaningful reasoning approaches.}},
author = {{Fleischer, Franz Yannik and Biehler, Rolf}},
issn = {{1863-9690}},
journal = {{ZDM – Mathematics Education}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Informal approaches to predictive modeling: fostering data literacy and critical engagement through decision tree construction}}},
doi = {{10.1007/s11858-026-01806-3}},
year = {{2026}},
}
@article{60491,
abstract = {{We investigate generalisations of 1-factorisations and hyperfactorisations of the complete graph $K_{2n}$. We show that they are special subsets of the association scheme obtained from the Gelfand pair $(S_{2n},S_2 \wr S_n)$. This unifies and extends results by Cameron (1976) and gives rise to new existence and non-existence results. Our methods involve working in the group algebra $\mathbb{C}[S_{2n}]$ and using the representation theory of $S_{2n}$.}},
author = {{Klawuhn, Lukas-André Dominik and Bamberg, John}},
journal = {{Algebraic Combinatorics}},
number = {{3}},
pages = {{789--809}},
title = {{{On the association scheme of perfect matchings and their designs}}},
doi = {{10.5802/alco.490}},
volume = {{9}},
year = {{2026}},
}