@unpublished{63394, abstract = {{We study the statistics of the number of real eigenvalues in the elliptic deformation of the real Ginibre ensemble. As the matrix dimension grows, the law of large numbers and the central limit theorem for the number of real eigenvalues are well understood, but the probabilities of rare events remain largely unexplored. Large deviation type results have been obtained only in extreme cases, when either a vanishingly small proportion of eigenvalues are real or almost all eigenvalues are real. Here, in both the strong and weak asymmetry regimes, we derive the probabilities of rare events in the moderate-to-large deviation regime, thereby providing a natural connection between the previously known regime of Gaussian fluctuations and the large deviation regime. Our results are new even for the classical real Ginibre ensemble.}}, author = {{Byun, Sung-Soo and Jalowy, Jonas and Lee, Yong-Woo and Schehr, Grégory}}, booktitle = {{arXiv:2511.09191}}, title = {{{Moderate-to-large deviation asymptotics for real eigenvalues of the elliptic Ginibre matrices}}}, year = {{2025}}, } @unpublished{63393, abstract = {{We study the evolution of zeros of high polynomial powers under the heat flow. For any fixed polynomial $P(z)$, we prove that the empirical zero distribution of its heat-evolved $n$-th power converges to a distribution on the complex plane as $n$ tends to infinity. We describe this limit distribution $μ_t$ as a function of the time parameter $t$ of the heat evolution: For small time, zeros start to spread out in approximately semicircular distributions, then intricate curves start to form and merge, until for large time, the zero distribution approaches a widespread semicircle law through the initial center of mass. The Stieltjes transform of the limit distribution $μ_t$ satisfies a self-consistent equation and a Burgers' equation. The present paper deals with general complex-rooted polynomials for which, in contrast to the real-rooted case, no free-probabilistic representation for $μ_t$ is available.}}, author = {{Höfert, Antonia and Jalowy, Jonas and Kabluchko, Zakhar}}, booktitle = {{arXiv:2512.17808}}, title = {{{Zeros of polynomial powers under the heat flow}}}, year = {{2025}}, } @inproceedings{63434, author = {{Hoffmann, Max}}, booktitle = {{Proceedings of the Fourteenth Congress of the European Society for Research in Mathematics Education (CERME14)}}, editor = {{Bosch, Marianna and Bolondi, Giorgio and Carreira, Susana and Michael, Gaidoschik and Camilla, Spagnolo}}, keywords = {{hoffmann, reviewed, proceedings}}, title = {{{Using scriptwriting as a response format for interface tasks: Exemplary analyses in the context of symmetry}}}, year = {{2025}}, } @article{63433, author = {{Hoffmann, Max}}, journal = {{mathematik lehren}}, number = {{253}}, pages = {{39--44}}, title = {{{Digitale Perspektiven auf das Heron-Verfahren}}}, doi = {{https://doi.org/10.5555/ml-253-2025_07}}, year = {{2025}}, } @article{54837, author = {{Claes, Leander and Lankeit, Johannes and Winkler, Michael}}, issn = {{1793-6314}}, journal = {{Mathematical Models and Methods in Applied Sciences}}, number = {{11}}, pages = {{2465--2512}}, publisher = {{World Scientific Pub Co Pte Ltd}}, title = {{{A model for heat generation by acoustic waves in piezoelectric materials: Global large-data solutions}}}, doi = {{10.1142/s0218202525500447}}, volume = {{35}}, year = {{2025}}, } @unpublished{63510, abstract = {{It has been shown recently that optimal control problems with the dynamical constraint given by a second order system admit a regular Lagrangian formulation. This implies that the optimality conditions can be obtained in a new form based on the variational approach. In this paper we extend the first order necessary optimality conditions obtained previously to second order optimality conditions. This results in a complete characterization of the optimality conditions in a new Lagrangian form.}}, author = {{Konopik, Michael and Leyendecker, Sigrid and Maslovskaya, Sofya and Sina Ober-Blöbaum, Sina Ober-Blöbaum and Almagro, Rodrigo T. Sato Martín de}}, booktitle = {{arXiv:2507.06024}}, title = {{{Second order optimality conditions in a new Lagrangian formulation for optimal control problems}}}, year = {{2025}}, } @article{59797, author = {{Konopik, Michael and T. Sato Martín de Almagro, Rodrigo and Maslovskaya, Sofya and Ober-Blöbaum, Sina and Leyendecker, Sigrid}}, journal = {{Journal of Nonlinear Science}}, number = {{11}}, title = {{{Variational integrators for a new Lagrangian approach to control affine systems with a quadratic Lagrange term}}}, doi = {{10.1007/s00332-025-10229-5}}, volume = {{36}}, year = {{2025}}, } @article{59799, author = {{Konopik, Michael and Leyendecker, Sigrid and Maslovskaya, Sofya and Ober-Blöbaum, Sina and T. Sato Martín de Almagro, Rodrigo}}, journal = {{Nonlinearity}}, number = {{11}}, title = {{{A new Lagrangian approach to optimal control of second-order systems}}}, doi = {{10.1088/1361-6544/ae1d08}}, volume = {{38}}, year = {{2025}}, } @article{53414, abstract = {{By constructing a non-empty domain of discontinuity in a suitable homogeneous space, we prove that every torsion-free projective Anosov subgroup is the monodromy group of a locally homogeneous contact Axiom A dynamical system with a unique basic hyperbolic set on which the flow is conjugate to the refraction flow of Sambarino. Under the assumption of irreducibility, we utilize the work of Stoyanov to establish spectral estimates for the associated complex Ruelle transfer operators, and by way of corollary: exponential mixing, exponentially decaying error term in the prime orbit theorem, and a spectral gap for the Ruelle zeta function. With no irreducibility assumption, results of Dyatlov-Guillarmou imply the global meromorphic continuation of zeta functions with smooth weights, as well as the existence of a discrete spectrum of Ruelle-Pollicott resonances and (co)-resonant states. We apply our results to space-like geodesic flows for the convex cocompact pseudo-Riemannian manifolds of Danciger-Gu\'eritaud-Kassel, and the Benoist-Hilbert geodesic flow for strictly convex real projective manifolds.}}, author = {{Delarue, Benjamin and Monclair, Daniel and Sanders, Andrew}}, journal = {{Geometric and Functional Analysis (GAFA)}}, pages = {{673–735}}, title = {{{Locally homogeneous Axiom A flows I: projective Anosov subgroups and exponential mixing}}}, doi = {{10.1007/s00039-025-00712-2}}, volume = {{35}}, year = {{2025}}, } @article{53412, abstract = {{Let $M$ be a symplectic manifold carrying a Hamiltonian $S^1$-action with momentum map $J:M \rightarrow \mathbb{R}$ and consider the corresponding symplectic quotient $\mathcal{M}_0:=J^{-1}(0)/S^1$. We extend Sjamaar's complex of differential forms on $\mathcal{M}_0$, whose cohomology is isomorphic to the singular cohomology $H(\mathcal{M}_0;\mathbb{R})$ of $\mathcal{M}_0$ with real coefficients, to a complex of differential forms on $\mathcal{M}_0$ associated with a partial desingularization $\widetilde{\mathcal{M}}_0$, which we call resolution differential forms. The cohomology of that complex turns out to be isomorphic to the de Rham cohomology $H(\widetilde{ \mathcal{M}}_0)$ of $\widetilde{\mathcal{M}}_0$. Based on this, we derive a long exact sequence involving both $H(\mathcal{M}_0;\mathbb{R})$ and $H(\widetilde{ \mathcal{M}}_0)$ and give conditions for its splitting. We then define a Kirwan map $\mathcal{K}:H_{S^1}(M) \rightarrow H(\widetilde{\mathcal{M}}_0)$ from the equivariant cohomology $H_{S^1}(M)$ of $M$ to $H(\widetilde{\mathcal{M}}_0)$ and show that its image contains the image of $H(\mathcal{M}_0;\mathbb{R})$ in $H(\widetilde{\mathcal{M}}_0)$ under the natural inclusion. Combining both results in the case that all fixed point components of $M$ have vanishing odd cohomology we obtain a surjection $\check \kappa:H^\textrm{ev}_{S^1}(M) \rightarrow H^\textrm{ev}(\mathcal{M}_0;\mathbb{R})$ in even degrees, while already simple examples show that a similar surjection in odd degrees does not exist in general. As an interesting class of examples we study abelian polygon spaces.}}, author = {{Delarue, Benjamin and Ramacher, Pablo and Schmitt, Maximilian}}, journal = {{Transformation Groups}}, title = {{{Singular cohomology of symplectic quotients by circle actions and Kirwan surjectivity}}}, doi = {{10.1007/s00031-025-09924-0}}, year = {{2025}}, } @article{63556, author = {{Biehler, Rolf and Engel, Joachim and Frischemeier, Daniel and Podworny, Susanne}}, journal = {{mathematica didactica}}, number = {{2}}, title = {{{Civic Statistical Literacy: Konzept und praxisnahe Umsetzung am Beispiel des Klimawandels}}}, doi = {{10.18716/ojs/md/2025.2297}}, volume = {{48}}, year = {{2025}}, } @unpublished{63569, abstract = {{Let $G$ be a totally disconnected locally compact (tdlc) group. The contraction group $\mathrm{con}(g)$ of an element $g\in G$ is the set of all $h\in G$ such that $g^n h g^{-n} \to 1_G$ as $n \to \infty$. The nub of $g$ can then be characterized as the intersection $\mathrm{nub}(g)$ of the closures of $\mathrm{con}(g)$ and $\mathrm{con}(g^{-1})$. Contraction groups and nubs provide important tools in the study of the structure of tdlc groups, as already evidenced in the work of G. Willis. It is known that $\mathrm{nub}(g) = \{1\}$ if and only if $\mathrm{con}(g)$ is closed. In general, contraction groups are not closed and computing the nub is typically a challenging problem. Maximal Kac-Moody groups over finite fields form a prominent family of non-discrete compactly generated simple tdlc groups. In this paper we give a complete description of the nub of any element in these groups.}}, author = {{Bischof, Sebastian and Marquis, Timothée}}, title = {{{Describing the nub in maximal Kac-Moody groups}}}, year = {{2025}}, } @unpublished{63568, abstract = {{In this article we work out the details of flat groups of the automorphism group of locally finite Bruhat-Tits buildings.}}, author = {{Bischof, Sebastian}}, title = {{{On flat groups in affine buildings}}}, year = {{2025}}, } @inproceedings{63571, abstract = {{Prüfungen sind ein wesentlicher Bestandteil des Mathematikunterrichts. Mündliche Prüfungsformate sind insbesondere in Abschlussprüfungen üblich, wurden aber bislang kaum untersucht. Dieses Projekt widmet sich dem Vorkommen und der Bedeutung verschiedener Wissensarten in mündlichen Prüfungen. Dazu soll auf Grundlage videografierter Prüfungsgespräche eine Taxonomie für abgefragte Wissensarten entwickelt werden. Der Vortrag präsentiert die Konzeption sowie erste Ergebnisse einer Vorstudie, die als Basis für eine vertiefte Analyse realer Prüfungen dient.}}, author = {{Hellmund, Johannes}}, booktitle = {{Beiträge zum Mathematikunterricht 2025}}, editor = {{Schick, L. and Platz, M. and Lambert, A.}}, location = {{Saarbrücken}}, pages = {{1417}}, publisher = {{WTM}}, title = {{{Mündliche Prüfungen im Mathematikunterricht – welche Arten des Wissens werden abgefragt?}}}, doi = {{10.17877/DE290R-25900}}, year = {{2025}}, } @article{34807, abstract = {{Let $M$ be a compact, real analytic manifold and $G$ be the Lie group of all real-analytic diffeomorphisms of $M$, which is modelled on the (DFS)-space ${\mathfrak g}$ of real-analytic vector fields on $M$. We study flows of time-dependent real-analytic vector fields on $M$ which are integrable functions in time, and their dependence on the time-dependent vector field. Notably, we show that the Lie group $G$ is $L^1$-regular in the sense that each $[\gamma]$ in $L^1([0,1],{\mathfrak g})$ has an evolution which is an absolutely continuous $G$-valued function on $[0,1]$ and smooth in $[\gamma]$. As tools for the proof, we develop several new results concerning $L^p$-regularity of infinite-dimensional Lie groups, for $1\leq p\leq \infty$, which will be useful also for the discussion of other classes of groups. Moreover, we obtain new results concerning the continuity and complex analyticity of non-linear mappings on open subsets of locally convex direct limits.}}, author = {{Glöckner, Helge}}, journal = {{Nonlinear Analysis}}, title = {{{Lie groups of real analytic diffeomorphisms are L^1-regular}}}, doi = {{10.1016/j.na.2024.113690}}, volume = {{252}}, year = {{2025}}, } @inproceedings{56298, abstract = {{In the general pattern formation (GPF) problem, a swarm of simple autonomous, disoriented robots must form a given pattern. The robots' simplicity imply a strong limitation: When the initial configuration is rotationally symmetric, only patterns with a similar symmetry can be formed [Yamashita, Suzyuki; TCS 2010]. The only known algorithm to form large patterns with limited visibility and without memory requires the robots to start in a near-gathering (a swarm of constant diameter) [Hahn et al.; SAND 2024]. However, not only do we not know any near-gathering algorithm guaranteed to preserve symmetry but most natural gathering strategies trivially increase symmetries [Castenow et al.; OPODIS 2022]. Thus, we study near-gathering without changing the swarm's rotational symmetry for disoriented, oblivious robots with limited visibility (the OBLOT-model, see [Flocchini et al.; 2019]). We introduce a technique based on the theory of dynamical systems to analyze how a given algorithm affects symmetry and provide sufficient conditions for symmetry preservation. Until now, it was unknown whether the considered OBLOT-model allows for any non-trivial algorithm that always preserves symmetry. Our first result shows that a variant of Go-to-the-Average always preserves symmetry but may sometimes lead to multiple, unconnected near-gathering clusters. Our second result is a symmetry-preserving near-gathering algorithm that works on swarms with a convex boundary (the outer boundary of the unit disc graph) and without holes (circles of diameter 1 inside the boundary without any robots).}}, author = {{Gerlach, Raphael and von der Gracht, Sören and Hahn, Christopher and Harbig, Jonas and Kling, Peter}}, booktitle = {{28th International Conference on Principles of Distributed Systems (OPODIS 2024)}}, editor = {{Bonomi, Silvia and Galletta, Letterio and Rivière, Etienne and Schiavoni, Valerio}}, isbn = {{978-3-95977-360-7}}, issn = {{1868-8969}}, keywords = {{Swarm Algorithm, Swarm Robots, Distributed Algorithm, Pattern Formation, Limited Visibility, Oblivious}}, location = {{Lucca, Italy}}, publisher = {{Schloss Dagstuhl -- Leibniz-Zentrum für Informatik}}, title = {{{Symmetry Preservation in Swarms of Oblivious Robots with Limited Visibility}}}, doi = {{10.4230/LIPIcs.OPODIS.2024.13}}, volume = {{324}}, year = {{2025}}, } @article{58532, author = {{Bullerjahn, Nils}}, journal = {{arXiv}}, title = {{{Error estimates for full discretization by an almost mass conservation technique for Cahn--Hilliard systems with dynamic boundary conditions}}}, doi = {{10.48550/ARXIV.2502.03847}}, year = {{2025}}, } @unpublished{58544, abstract = {{We introduce a new classification of multimode states with a fixed number of photons. This classification is based on the factorizability of homogeneous multivariate polynomials and is invariant under unitary transformations. The classes physically correspond to field excitations in terms of single and multiple photons, each of which being in an arbitrary irreducible superposition of quantized modes. We further show how the transitions between classes are rendered possible by photon addition, photon subtraction, and photon-projection nonlinearities. We explicitly put forward a design for a multilayer interferometer in which the states for different classes can be generated with state-of-the-art experimental techniques. Limitations of the proposed designs are analyzed using the introduced classification, providing a benchmark for the robustness of certain states and classes. }}, author = {{Kopylov, Denis and Offen, Christian and Ares, Laura and Wembe Moafo, Boris Edgar and Ober-Blöbaum, Sina and Meier, Torsten and Sharapova, Polina and Sperling, Jan}}, title = {{{Multiphoton, multimode state classification for nonlinear optical circuits }}}, year = {{2025}}, } @article{58947, author = {{Krüger, Katja and Werth, Gerda}}, issn = {{0732-3123}}, journal = {{The Journal of Mathematical Behavior}}, publisher = {{Elsevier BV}}, title = {{{Mathematics education for girls in Prussia 1890–1925}}}, doi = {{10.1016/j.jmathb.2025.101242}}, volume = {{79}}, year = {{2025}}, } @unpublished{58953, abstract = {{In this article, we investigate symmetry properties of distributed systems of mobile robots. We consider a swarm of n robots in the OBLOT model and analyze their collective Fsync dynamics using of equivariant dynamical systems theory. To this end, we show that the corresponding evolution function commutes with rotational and reflective transformations of R^2. These form a group that is isomorphic to O(2) x S_n, the product group of the orthogonal group and the permutation on n elements. The theory of equivariant dynamical systems is used to deduce a hierarchy along which symmetries of a robot swarm can potentially increase following an arbitrary protocol. By decoupling the Look phase from the Compute and Move phases in the mathematical description of an LCM cycle, this hierarchy can be characterized in terms of automorphisms of connectivity graphs. In particular, we find all possible types of symmetry increase, if the decoupled Compute and Move phase is invertible. Finally, we apply our results to protocols which induce state-dependent linear dynamics, where the reduced system consisting of only the Compute and Move phase is linear.}}, author = {{Gerlach, Raphael and von der Gracht, Sören}}, booktitle = {{arXiv:2503.07576}}, keywords = {{dynamical systems, coupled systems, distributed computing, robot swarms, autonomous mobile robots, symmetry, equivariant dynamics}}, pages = {{23}}, title = {{{Analyzing Symmetries of Swarms of Mobile Robots Using Equivariant Dynamical Systems}}}, year = {{2025}}, }