@unpublished{63135,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}},
title = {{{Coxeter-Dynkin algebras of canonical type}}},
year = {{2025}},
}
@article{63649,
author = {{Glöckner, Helge and Schmeding, Alexander and Suri, Ali}},
issn = {{2972-4589}},
journal = {{Geometric Mechanics}},
number = {{04}},
pages = {{383--437}},
publisher = {{World Scientific Pub Co Pte Ltd}},
title = {{{Manifolds of continuous BV-functions and vector measure regularity of Banach–Lie groups}}},
doi = {{10.1142/s2972458925500029}},
volume = {{01}},
year = {{2025}},
}
@inproceedings{63697,
author = {{Stallmeister, Lea and Rezat, Sebastian}},
booktitle = {{Beiträge zum Mathematikunterricht 2025. 58. Jahrestagung der Gesellschaft für Didaktik der Mathematik}},
editor = {{Schick, Lisa and Platz, Melanie and Lambert, Anselm}},
location = {{Universität des Saarlandes, Saarbrücken}},
publisher = {{WTM-Verlag}},
title = {{{Die Bedeutung des Mathematikschulbuchs in Zeiten der Ressourcenvielfalt}}},
doi = {{10.17877/DE290R-26373}},
year = {{2025}},
}
@inproceedings{62062,
author = {{Neufeld, Inga and Häsel-Weide, Uta}},
booktitle = {{Proceedings of the Fourteenth Congress of the European Society for Research in Mathematics Education (CERME14)}},
editor = {{Bosch, M. and Bolondi, G. and Carreira, S. and Spagnolo, C. and Gaidoschik, M.}},
location = {{Bozen, Italy}},
title = {{{Learning support practices in the fostering of basic arithmetic skills}}},
year = {{2025}},
}
@inproceedings{62063,
author = {{Häsel-Weide, Uta and Nührenbörger, Marcus}},
booktitle = {{Proceedings of the Fourteenth Congress of the European Society for Research in Mathematics Education (CERME14)}},
editor = {{Bosch, M. and Bolondi, G. and Carreira, S. and Spagnolo, C. and Gaidoschik, M.}},
location = {{Bozen, Italy}},
title = {{{Practices in math discourses in inclusive primary school}}},
year = {{2025}},
}
@inbook{63730,
author = {{Bruns, Julia and Gasteiger, Hedwig and Lastering, Bernd and Schopferer, Theresa and Zech, Detlev}},
booktitle = {{25 Jahre Berufskolleg - Wegspuren und Zukunftspfade}},
editor = {{Pudenz, Stephanie and Schoell, Oliver and Cleef, Maria}},
pages = {{175--188}},
publisher = {{wbv}},
title = {{{Frühe mathematische Bildung als Ausbildungsinhalt der Erzieherinnen- und Erzieher-Ausbildung stärken}}},
year = {{2025}},
}
@article{55459,
author = {{Bullerjahn, Nils and Kovács, Balázs}},
journal = {{IMA Journal of Numerical Analysis}},
title = {{{Error estimates for full discretization of Cahn--Hilliard equation with dynamic boundary conditions}}},
doi = {{10.1093/imanum/draf009}},
year = {{2025}},
}
@article{53141,
author = {{Edelmann, Dominik and Kovács, Balázs and Lubich, Christian}},
journal = {{IMA Journal of Numerical Analysis}},
number = {{5}},
pages = {{2581----2627}},
title = {{{Numerical analysis of an evolving bulk--surface model of tumour growth}}},
doi = {{10.1093/imanum/drae077}},
volume = {{45}},
year = {{2025}},
}
@article{55781,
abstract = {{In this paper, we prove that spatially semi-discrete evolving finite element
method for parabolic equations on a given evolving hypersurface of arbitrary
dimensions preserves the maximal $L^p$-regularity at the discrete level. We
first establish the results on a stationary surface and then extend them, via a
perturbation argument, to the case where the underlying surface is evolving
under a prescribed velocity field. The proof combines techniques in evolving
finite element method, properties of Green's functions on (discretised) closed
surfaces, and local energy estimates for finite element methods}},
author = {{Bai, Genming and Kovács, Balázs and Li, Buyang}},
journal = {{IMA Journal of Numerical Analysis}},
title = {{{Maximal regularity of evolving FEMs for parabolic equations on an evolving surface}}},
doi = {{10.1093/imanum/draf082.}},
year = {{2025}},
}
@article{56717,
abstract = {{We establish a multiresolution analysis on the space $\text{Herm}(n)$ of
$n\times n$ complex Hermitian matrices which is adapted to invariance under
conjugation by the unitary group $U(n).$ The orbits under this action are
parametrized by the possible ordered spectra of Hermitian matrices, which
constitute a closed Weyl chamber of type $A_{n-1}$ in $\mathbb R^n.$ The space
$L^2(\text{Herm}(n))^{U(n)}$ of radial, i.e. $U(n)$-invariant $L^2$-functions
on $\text{Herm}(n)$ is naturally identified with a certain weighted $L^2$-space
on this chamber.
The scale spaces of our multiresolution analysis are obtained by usual dyadic
dilations as well as generalized translations of a scaling function, where the
generalized translation is a hypergroup translation which respects the radial
geometry. We provide a concise criterion to characterize orthonormal wavelet
bases and show that such bases always exist. They provide natural orthonormal
bases of the space $L^2(\text{Herm}(n))^{U(n)}.$
Furthermore, we show how to obtain radial scaling functions from classical
scaling functions on $\mathbb R^{n}$. Finally, generalizations related to the
Cartan decompositions for general compact Lie groups are indicated.}},
author = {{Langen, Lukas and Rösler, Margit}},
journal = {{Indagationes Mathematicae}},
number = {{6}},
pages = {{1671--1694}},
publisher = {{Elsevier}},
title = {{{Multiresolution analysis on spectra of hermitian matrices}}},
volume = {{36}},
year = {{2025}},
}
@article{64289,
abstract = {{Abstract
Motivated by asymptotic symmetry groups in general relativity, we consider projective unitary representations
$$\overline{\rho }$$
ρ
¯
of the Lie group
$${{\,\textrm{Diff}\,}}_c(M)$$
Diff
c
(
M
)
of compactly supported diffeomorphisms of a smooth manifold M that satisfy a so-called generalized positive energy condition. In particular, this captures representations that are in a suitable sense compatible with a KMS state on the von Neumann algebra generated by
$$\overline{\rho }$$
ρ
¯
. We show that if M is connected and
$$\dim (M) > 1$$
dim
(
M
)
>
1
, then any such representation is necessarily trivial on the identity component
$${{\,\textrm{Diff}\,}}_c(M)_0$$
Diff
c
(
M
)
0
. As an intermediate step towards this result, we determine the continuous second Lie algebra cohomology
$$H^2_\textrm{ct}(\mathcal {X}_c(M), \mathbb {R})$$
H
ct
2
(
X
c
(
M
)
,
R
)
of the Lie algebra of compactly supported vector fields. This is subtly different from Gelfand–Fuks cohomology in view of the compact support condition.}},
author = {{Janssens, Bas and Niestijl, Milan}},
issn = {{0010-3616}},
journal = {{Communications in Mathematical Physics}},
number = {{2}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Generalized Positive Energy Representations of the Group of Compactly Supported Diffeomorphisms}}},
doi = {{10.1007/s00220-024-05226-w}},
volume = {{406}},
year = {{2025}},
}
@article{50299,
abstract = {{A finite classical polar space of rank $n$ consists of the totally isotropic
subspaces of a finite vector space over $\mathbb{F}_q$ equipped with a
nondegenerate form such that $n$ is the maximal dimension of such a subspace. A
$t$-$(n,k,\lambda)$ design in a finite classical polar space of rank $n$ is a
collection $Y$ of totally isotropic $k$-spaces such that each totally isotropic
$t$-space is contained in exactly $\lambda$ members of $Y$. Nontrivial examples
are currently only known for $t\leq 2$. We show that $t$-$(n,k,\lambda)$
designs in polar spaces exist for all $t$ and $q$ provided that
$k>\frac{21}{2}t$ and $n$ is sufficiently large enough. The proof is based on a
probabilistic method by Kuperberg, Lovett, and Peled, and it is thus
nonconstructive.}},
author = {{Weiß, Charlene}},
journal = {{Des. Codes Cryptogr.}},
pages = {{971 -- 981}},
title = {{{Nontrivial $t$-designs in polar spaces exist for all $t$}}},
doi = {{10.1007/s10623-024-01471-1}},
volume = {{93}},
year = {{2025}},
}
@article{59258,
author = {{Winkler, Michael}},
issn = {{0095-4616}},
journal = {{Applied Mathematics & Optimization}},
number = {{2}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Rough Data in an Evolution System Generalizing 1D Thermoviscoelasticity with Temperature-Dependent Parameters}}},
doi = {{10.1007/s00245-025-10243-9}},
volume = {{91}},
year = {{2025}},
}
@misc{64736,
booktitle = {{J. Lie Theory}},
editor = {{Frahm, Jan and Glöckner, Helge and Hilgert, Joachim and Olafsson, Gestur}},
number = {{4}},
title = {{{Special issue of Journal of Lie Theory dedicated to Karl-Hermann Neeb on the occasion of his 60th birthday}}},
volume = {{35}},
year = {{2025}},
}
@phdthesis{64770,
author = {{Pinaud, Matthieu}},
title = {{{Manifold of mappings and regularity properties of half-Lie groups}}},
doi = {{10.17619/UNIPB/1-2211}},
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}},
}