Tootfinder

Warum muss ich hier spontan an die Causa Lothar König denken? 🤔
https://www.saechsische.de/sachsen/polizei-zieht-adenauer-bus-wegen-technischer-maengel-aus-dem-verkehr-2VCV4VMJABCDRLMXOOSB4AQ5W4.html

Polizei zieht „Adenauer-Bus“ wegen technischer Mängel aus dem Verkehr
Ein Gutachter der Dekra hat den „Adenauer-Bus“ als nicht verkehrssicher eingestuft. Das Zentrum für Politische Schönheit kann das Fahrzeug dadurch nicht mehr nutzen - bis auf Weiteres.

Cubic Fourfolds with an Order-$7$ Automorphism
Xuancong He, Yi Li, Shihao Wang, Zhiwei Zheng
https://arxiv.org/abs/2509.26359 https://arxiv.org/pdf/2509.26…

Cubic Fourfolds with an Order-$7$ Automorphism
We study smooth cubic fourfolds admitting an automorphism of order $7$. It is known that the possible symplectic automorphism groups of such cubic fourfolds are precisely $F_{21}$, $\mathrm{PSL}(2,\mathbb{F}_7)$, and $A_7$. In this paper, we determine all possible full automorphism groups of smooth cubic fourfolds with an automorphism of order $7$. We also investigate the moduli spaces of cubic fourfolds whose automorphism group is either $F_{21}$ or $\mathrm{PSL}(2,\mathbb{F}_7)$, describing t…

Automorphic orbits in free groups: recent progress
Vladimir Shpilrain
https://arxiv.org/abs/2510.00889 https://arxiv.org/pdf/2510.00889

Automorphic orbits in free groups: recent progress
In this survey, we describe recent progress on asymptotic properties of various automorphic orbits in free groups. In particular, we address the problem of counting potentially positive elements of a given length. We also discuss complexity (worst-case, average-case, and generic-case) of Whitehead's automorphism problem and relevant properties of automorphic orbits, including orbit-blocking words.

The existence of unexpected automorphisms in direct product graphs
Xiaomeng Wang, Yan-Li Qin, Binzhou Xia
https://arxiv.org/abs/2509.26170 https://arxiv.or…

The existence of unexpected automorphisms in direct product graphs
A pair of graphs $(Γ,Σ)$ is called unstable if their direct product $Γ\timesΣ$ admits automorphisms not from $\mathrm{Aut}(Γ)\times\mathrm{Aut}(Σ)$, and such automorphisms are said to be unexpected. The stability of a graph $Γ$ refers to that of $(Γ,K_2)$. While the stability of individual graphs has been relatively well studied, much less is known for graph pairs. In this paper, we propose a conjecture that provides the best possible reduction of the stability of a graph pair to the st…

Die Polizei versucht wohl grade mit einem Kran die Boxen vom #Adenauer #SRP des #ZPS @…

Önskar er alla en fin allhelgonahelg. #díademuertos

A dichotomy for derivations and automorphisms of C*-algebras
Martino Lupini
https://arxiv.org/abs/2508.21726 https://arxiv.org/pdf/2508.21726

A dichotomy for derivations and automorphisms of C*-algebras
Building on previous work of Kadison--Ringrose, Elliott, Akemann--Pedersen, and this author, we prove a dichotomy for the relation of outer equivalence of derivations and unitary equivalence of derivable automorphisms for a separable C*-algebra $A$: either such relations are trivial, or the relation $E_{0}^{\mathbb{N}}$ of tail equivalence of countably many binary sequences is reducible to them. When $A$ is furthermore \emph{unital}, this implies that $A$ has no outer derivation if and only if …

Fact check: Trump makes numerous false claims to generals and admirals, some about the military (Daniel Dale/CNN)
https://www.cnn.com/2025/09/30/politics/fact-check-trump-military-speech
http://www.memeorandum.com/250930/p137#a250930p137

Unboundedness for motivic invariants of birational automorphisms
Hsueh-Yung Lin, Evgeny Shinder
https://arxiv.org/abs/2510.00290 https://arxiv.org/pdf/2510…

Unboundedness for motivic invariants of birational automorphisms
We introduce horizontal and vertical motivic invariants of birational maps between rational dominant maps and study their basic properties. As a first application, we show that the (usual) motivic invariants vanish for birational automorphisms of threefolds over algebraically closed fields of characteristic zero. On the other hand, we prove that the motivic invariants of the birational automorphism group of many types of varieties, including projective spaces of dimension at least four over a f…

Automorphism Groups of the $PSL_2(q)$ Commuting Involution Graphs
James Bryden, Peter Rowley
https://arxiv.org/abs/2509.25901 https://arxiv.org/pdf/2509.25…

Automorphism Groups of the $PSL_2(q)$ Commuting Involution Graphs
Given a finite group $G$ and a conjugacy class of involutions $X$ of $G$, we define the commuting involution graph $\mathcal{C}(G,X)$ to be the graph with vertex set $X$ and $x,y \in X$ adjacent if and only if $x \neq y$ and $xy =yx$. In this paper the automorphism group of the graph $\mathcal{C}(G,X)$ is determined when $G = PSL_2(q)$.