L p Asymptotics for the Heat Equation on Symmetric Spaces for Non-symmetric Solutions - Papageorgiou, Efthymia (International Mathematics Research Notices)
Abstract The main goal of this work is to study the $L^{p}$-asymptotic behavior of solutions to the heat equation on arbitrary rank Riemannian symmetric spaces of non-compact-type $G/K$ for non-bi-$K$ invariant initial data. For initial data $u_{0}$ compactly supported or in a weighted $L^{1}(G/K)$ space with a weight depending on $p\in [1, \infty ]$, we introduce a mass function $M_{p}(u_{0})(\cdot )$, and prove that if $h_{t}$ is the heat kernel on $G/K$, then $$ \begin{align*} &\|h_t\|_p^{-1}\,\|u_0\ast h_t \, - \,M_p(u_0)(\cdot)\,h_t\|_p \rightarrow 0 \quad \textrm{as} \quad t\rightarrow \infty.\end{align*} $$ Interestingly, the $L^{p}$ heat concentration leads to completely different expressions of the mass function for $1\leq p <2$ and $2\leq p\leq \infty $. If we further assume that the initial data are bi-$K$-invariant, then our mass function boils down to the constant $\int _{G/K}u_{0}$ in the case $p=1$, and more generally to $\mathcal{H}{u_{0}}(i\rho (2/p-1))$ if $1\leq p<2$, and to $\mathcal{H}{u_{0}}(0)$ if $2\leq p \leq \infty $. Thus, we improve upon results by Vázquez, Anker et al., and Naik et al., clarifying the nature of the problem.

Blow-up exponents and a semilinear elliptic equation for the fractional Laplacian on hyperbolic spaces - Bruno, Tommaso; Papageorgiou, Efthymia (arXiv:2509.12349)
Let $\mathbb{H}^n$ be the $n$-dimensional real hyperbolic space, $Δ$ its nonnegative Laplace--Beltrami operator whose bottom of the spectrum we denote by $λ_{0}$, and $σ\in (0,1)$. The aim of this paper is twofold. On the one hand, we determine the Fujita exponent for the fractional heat equation \[\partial_{t} u + Δ^σu = e^{βt}|u|^{γ-1}u,\] by proving that nontrivial positive global solutions exist if and only if $γ\geq 1 + β/ λ_{0}^σ$. On the other hand, we prove the existence of non-negative, bounded and finite energy solutions of the semilinear fractional elliptic equation \[ Δ^σ v - λ^σ v - v^γ=0 \] for $0\leq λ\leq λ_{0}$ and $1<γ< \frac{n+2σ}{n-2σ}$. The two problems are known to be connected and the latter, aside from its independent interest, is actually instrumental to the former. \smallskip At the core of our results stands a novel fractional Poincaré-type inequality expressed in terms of a new scale of $L^{2}$ fractional Sobolev spaces, which sharpens those known so far, and which holds more generally on Riemannian symmetric spaces of non-compact type. We also establish an associated Rellich--Kondrachov-like compact embedding theorem for radial functions, along with other related properties.

Freudig in die Schlacht - Emotionen als Codes für die recta intentio im gerechten Krieg (8.- 10. Jahrhundert) - Foerster, Anne (Emotionen im Krieg - Krieg der Emotionen)

Co-Designing NVM-based Systems for Machine Learning and In-memory Search Applications - Henkel, Jörg; Siddhu, Lokesh; Nassar, Hassan; Bauer, Lars; Chen, Jian-Jia; Hakert, Christian; Seidl, Tristan; Chen, Kuan Hsun; Hu, Xiaobo Sharon; Li, Mengyuan; Yang, Chia-Lin; Wei, Ming-Liang (Proceedings of the 43rd IEEE/ACM International Conference on Computer-Aided Design)

InTreeger: An End-to-End Framework for Integer-Only Decision Tree Inference

Statistics and data science education as a vehicle for empowering citizens–short summary of a survey - Biehler, Rolf; Kawakami, Takashi; Lampen, Erna; Weiland, Travis; Zapata-Cardona, Lucía (European Mathematical Society Magazine)

Algebraic Geometry of the Multilayer Model of the Fractional Quantum Hall Effect on a Torus - Burban, Igor; Klevtsov, Semyon (Communications in Mathematical Physics)
Abstract In 1993 Keski-Vakkuri and Wen introduced a model for the fractional quantum Hall effect based on multilayer two-dimensional electron systems satisfying quasi-periodic boundary conditions. Such a model is essentially specified by a choice of a complex torus E and a symmetric positively definite matrix K of size g with non-negative integral coefficients, satisfying some further constraints. The space of the corresponding wave functions turns out to be $$δ $$ δ -dimensional, where $$δ $$ δ is the determinant of K . We construct a hermitian holomorphic bundle of rank $$δ $$ δ on the abelian variety A (which is the g -fold product of the torus E with itself), whose fibres can be identified with the space of wave function of Keski-Vakkuri and Wen. A rigorous construction of this “magnetic bundle” involves the technique of Fourier–Mukai transforms on abelian varieties. The constructed bundle turns out to be simple and semi-homogeneous and it can be equipped with two different (and natural) hermitian metrics: the one coming from the center-of-mass dynamics and the one coming from the Hilbert space of the underlying many-body system. We prove that the canonical Bott–Chern connection of the first hermitian metric is always projectively flat and give sufficient conditions for this property for the second hermitian metric.

Some aspects of the theory of nodal orders - Burban, Igor; Drozd, Yuriy (Contemporary Mathematics)
In this paper, we elaborate ring theoretic properties of nodal orders. In particular, we prove that they are closed under taking crossed products with finite groups.

Exceptional hereditary curves and real curve orbifolds - Burban, Igor (Algebra and Discrete Mathematics)

Norms of wave functions for FQHE models on a torus - Burban, Igor; Klevtsov, Semyon (Contemporary Mathematics)
The goal of this paper is to give an explicit computation of the curvature of the magnetic vector bundle of the multi-layer model of the fractional quantum Hall effect on a torus. We also obtain concrete formulae for the norms of the corresponding wave functions arising in such models.

Logarithmic concavity of bimatroids - Röhrle, Felix; Ulirsch, Martin (Annals of Combinatorics)
Abstract A bimatroid is a matroid-like generalization of the collection of regular minors of a matrix. In this article, we use the theory of Lorentzian polynomials to study the logarithmic concavity of natural sequences associated with bimatroids. Bimatroids can be used to characterize morphisms of matroids and this observation (originally due to Kung) allows us to prove a weak version of logarithmic concavity of the number of bases of a morphism of matroids. This is weaker than the original result by Eur and Huh; it nevertheless provides us with a new perspective on Mason’s log-concavity conjecture for independent sets of matroids. We finally show that for realizable bimatroids, the regular minor polynomial is a volume polynomial. Applied to morphisms of matroids, this shows that the weak basis generating polynomial of a morphism is a volume polynomial; this confirms a conjecture of Eur–Huh for morphisms of nullity $$\le 1$$ ≤ 1 and gives an algebro-geometric explanation for Mason’s log-concavity conjecture in the realizable case.

An Abel-Jacobi theorem for metrized complexes of Riemann surfaces - Hofmann, Maximilian C. E.; Ulirsch, Martin (Advances in Geometry)
Abstract Motivated by the recent surge of interest in the geometry of hybrid spaces, we prove an Abel–Jacobi theorem for a metrized complex of Riemann surfaces, generalizing both the classical Abel–Jacobi theorem and its tropical analogue.

Tropicalization of toric prevarieties - Küronya, Alex; Souza, Pedro; Ulirsch, Martin (EMS Series of Congress Reports)

Methodenentwicklung zur Prognose der richtungsabhängigen Eigenschaftsänderungen von Klebverbindungen aufgrund von Relativverschiebungen während der Aushärtung - Beule, Felix

Complexity and Criticality in Neuro-Inspired Reservoirs - van der Vlag, Michiel; Yegenoglu, Alper; Jimenez-Romero, Cristian; Morrison, Abigail; Diaz, Sandra (Lecture Notes in Computer Science)

Ansprüche an eine Fortbildung zur analytischen Geometrie - Herrmann, Janine (Beiträge zum Mathematikunterricht 2024)

Disruptive Imaginations: Chronotopic Time Loops and Environmental Agency in Sky: Children of the Light - Skuratova, Angelina (Video Game Ecologies and Culture)

A Quantitative Guide to Navigate Speed/Accuracy Tradeoffs in System Level Design of RISC-V Processor Grids - Luchterhandt, Lars; Govindasamy, Vivek; Wang, Yutong; Scheytt, Christoph; Müller, Wolfgang; Dömer, Rainer (2025 Forum on Specification & Design Languages (FDL))

Trust the process?! Innovations- und Transferprozesse gestalten - Breuing, Friederike; Daniel-Söltenfuß, Desiree; Kückmann, Marie-Ann

Sprache(n) in Ausbildung und Beruf – aktuelle Forschungsfragen und -projekte.