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Mariposa Fire
Northbound 101 South of Calle Mariposa Reina,
Santa Barbara County, CA
https://share.watchduty.org/i/51947?ts=1750206799000

Watch Duty - Wildfire Maps & Alerts
Real-time information about wildfire and firefighting efforts nearby

Recursive characterisation of skew morphisms of finite cyclic groups
Martin Bachrat\'y, Michal Hagara
https://arxiv.org/abs/2506.11626 https://

Recursive characterisation of skew morphisms of finite cyclic groups
A skew morphism of a finite group $G$ is an element $φ$ of $\mathrm{Sym}(G)$ preserving the identity element of $G$ and having the property that for each $a\in G$ there exists a non-negative integer $i_a$ such that $φ(ab)=φ(a)φ^{i_a}(b)$ for all $b\in G$. In this paper we show that if a skew morphism $φ$ of $\mathbb{Z}_n$ is not an automorphism of $\mathbb{Z}_n$, then it is uniquely determined by a triple $(h,α,β)$ where $h$ is an element of $\mathbb{Z}_n$, $α$ is a skew morphism of $\m…

Bicategories of Lax Fractions
Graham Manuell, Lurdes Sousa
https://arxiv.org/abs/2507.12044 https://arxiv.org/pdf/2507.12044

Bicategories of Lax Fractions
The well-known calculus of fractions of Gabriel and Zisman provides a convenient way to formally invert morphisms in a category. This was extended to bicategories by Pronk. On the other hand, the second author has developed a calculus of lax fractions for order-enriched categories that formally turns a given class of morphisms into left adjoint right inverses. We extend these constructions by presenting a calculus of lax fractions for 2-categories that formally turns a class of morphisms and ps…

Words avoiding the morphic images of most of their factors
Pascal Ochem, Matthieu Rosenfeld
https://arxiv.org/abs/2506.13368 https://…

Words avoiding the morphic images of most of their factors
We say that a finite factor $f$ of a word $w$ is \emph{imaged} if there exists a non-erasing morphism $m$, distinct from the identity, such that $w$ contains $m(f)$. We show that every infinite binary word contains an imaged factor of length at least 6 and that 6 is best possible. We show that every infinite binary word contains at least 36 distinct imaged factors and that 36 is best possible.

Tubi expands its partnerships with MrBeast and other creators, and hires former TikTok executive Kudzi Chikumbu as VP of creator partnerships (Caitlin Huston/The Hollywood Reporter)
https://www.hollywoodreporter.com/business/digital/tubi-expands-m…

Tubi Expands Partnerships With MrBeast, Other Creators
The company has also hired TikTok executive Kudzi Chikumbu to manage partnerships with creators on the platform.

🇺🇦 #NowPlaying on KEXP's #VarietyMix
maria bc:
🎵 ***
#mariabc
https://mariabc.bandcamp.com/track/-

Was für ein Verlust für die Kölner Kinoszene. Bernhard Marsch, zentrale Figur des Filmclub 813, ist Sonntagabend bei einem Unfall verstorben.
https://www.filmstiftung.de/news/bernhard-marsch-verstorben/

Bernhard Marsch verstorben - Film und Medien Stiftung NRW
Der Kölner Regisseur, Drehbuchautor, Filmproduzent und Schauspieler Bernhard Marsch ist überraschend bei einem tragischen Unfall im Alter von 63 Jahren verstorben.Der 1962 geborene Filmemacher war eine engagierte Persönlichkeit der Kölner Filmszene. 1990 gehörte Marsch zu den Gründungsmitgliedern des Filmclub 813, dessen langjähriger Vorsitzender er war. Der Filmclub wurde mehrfach mit dem Kinematheksverbundspreis ausgezeichnet und gilt als fester Bestandteil der Kölner Filmkultur.

🇺🇦 #NowPlaying on KEXP's #MiddayShow
Oasis:
🎵 Wonderwall
#Oasis
https://lorenzomariagiovanni.bandcamp.com/album/il-muro-delle-meraviglie-oasis-wonderwall-cover
https://open.spotify.com/track/0A6sqSxlqml1wjQLjuM4BH

Note on the linearisation of finite abelian groups
Aur\'elien Djament (CNRS, LAGA)
https://arxiv.org/abs/2507.13047 https://arxiv…

Note on the linearisation of finite abelian groups
If $K$ is a field \textit{with enough roots of unity} and $V$ an abelian group, the $K$-algebra $K[V]$ of the group $V$ is split semisimple, so that the canonical morphism $K[V]\to K^{V^\sharp}$, where $V^\sharp$ denotes the dual group of $V$ (which may be seen as Hom$(V,K^\times)$), is an isomorphism of $K$-algebras. If one removes the assumption that $K$ has enough roots of unity, one can easily deduce from it (by using a base change and Krull-Schmidt) that it remains a $K$-linear isomorphism…

🇺🇦 #NowPlaying on KEXP's #Early
Pickwick:
🎵 Hacienda Motel
#Pickwick
https://fremontabbey.bandcamp.com/track/hacienda-motel-acapella
https://open.spotify.com/track/17MRv4jLAOLThXK1VCzF4E