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On relative cuspidality
Nadir Matringe
https://arxiv.org/abs/2506.08393 https://arxiv.org/pdf/2506.08393

On relative cuspidality
Let $(\mathbb{G},\mathbb{H})$ be a symmetric pair of reductive groups over a $p$-adic field with $p\neq 2$, attached to the involution $θ$. Under the assumption that there exists a maximally $θ$-split torus in $\mathbb{G}$, which is anisotropic modulo its intersection with the split component of $\mathbb{G}$, we extend Beuzart-Plessis' proof of existence of cuspidal representations, and prove that $\mathbb{G}(F)$ admits strongly relatively cuspidal representations. This confirms expectations …

This https://arxiv.org/abs/2410.02734 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Computations directly on the cuspidal cohomology of congruence subgroups of $\mathrm{SL}(3, \mathbb{Z})$
In their 1984 work, Ash, Grayson, and Green compute the action of Hecke operators on a certain subspace of the cohomology of low-level congruence subgroups of $\mathsf{SL}(3, \mathbb{Z})$. This subspace contains the cuspidal cohomology, which is of primary interest. We extend their work, introducing a method that allows for computing the action of Hecke operators directly on the cuspidal cohomology. Using this method, we obtain data for prime level less than 2400, finding six additional levels …

For all the German speakers in my network: this wonderful and entertaining podcast by ZEIT Wissen takes my research on workplace environments and makes it personal by walking through their own offices, assessing them and checking in with staff on how they feel
The big question: which office form is best? Single offices, shared or open-plan? Assigned desks or activity based working?
Must listen! 👏🏻

Einzelbüro, Großraum, Zuhause? Wo der Mensch am besten arbeitet
ZEIT WISSEN. Woher weißt Du das? · Episode

Die ePetition 179398 an den Bundestag aus dem Bereich Bundesverfassungsgerichtsgesetz mit dem Titel
Reform des Bundesverfassungsgerichts
kann bis zum Mittwoch 16. Juli 2025 01:00 UTC mitgezeichnet werden und lautet
Mit der Petition wird eine Reform des Bundesverfassungsgerichts gefordert. Das Bundesverfassungsgericht sollte nicht nur angerufen werden können, sondern sollte auch proaktiv auf Verstöße reagieren können. Als Richter sollten nur Juristen eingesetzt werden, die k…

I bought Rosemary's Baby (eBook). I've always wondered 🤷‍♂️ I've never seen the movie either. The funny thing is, it came as a connection after browsing through the Beastie Boys Wikipedia page, following the path:
Beasty Boys -> Ad-Rock -> Molly Ringwald -> Tempest (1982 film) -> John Cassavetes (1929 - 1989) -> Rosemary's Baby (1968 film) -> Ira Levin (1929 - 2007).
...and then finding out there's a pricier, DRM-ed EPUB2 (2011) vs a little b…

Cowboys' most significant move this offseason isn't George Pickens, says analyst https://www.sportingnews.com/us/nfl/dallas-cowboys/news/cowboys-most-significant-move-offsea…

🇺🇦 #NowPlaying on KEXP's #ElSonido
Mirror Revelations:
🎵 Break the Circles
#MirrorRevelations
https://mirrorrevelations.bandcamp.com/track/break-the-circles
https://open.spotify.com/track/47CSISI1Bfy3A4dAsBIvwN

On a nonlinear Schr\"odinger-Bopp-Podolsky system in the zero mass case: functional framework and existence
Erasmo Caponio, Pietro d'Avenia, Alessio Pomponio, Gaetano Siciliano, Lianfeng Yang
https://arxiv.org/abs/2506.09752

On a nonlinear Schrödinger-Bopp-Podolsky system in the zero mass case: functional framework and existence
In this paper, we consider in $\mathbb{R}^3$ the following zero mass Schrödinger-Bopp-Podolsky system \[ \begin{cases} -Δu +q^2ϕu=|u|^{p-2}u\\ -Δϕ+a^2Δ^2ϕ=4πu^2 \end{cases} \] where $a>0$, $q\ne 0$ and $p\in (3,6)$. Inspired by [Ruiz, Arch. Ration. Mech. Anal. 198 (2010)], we introduce a Sobolev space $\mathcal{E}$ endowed with a norm containing a nonlocal term. Firstly, we provide some fundamental properties for the space $\mathcal{E}$ including embeddings into Lebesgue space…

Russland will auch in Zukunft friedliche Länder tyrannisieren: Kein Kriegsende ohne Stopp der Nato-Osterweiterung https://www.n-tv.de/politik/13-44-Moskau-Kein-Kriegsende-ohne-Stopp-der-Nato-Osterweiterung--article23143824.html

Ukraine-Krieg im Liveticker: +++ 13:44 Moskau: Kein Kriegsende ohne Stopp der Nato-Osterweiterung +++
Lesen Sie alle aktuellen Entwicklungen und Nachrichten über den russischen Angriffskrieg auf die Ukraine im Liveticker von ntv.de.

Congruence conditions for the mod $\lambda$ values of the Fourier coefficients of classical eigenforms
Michael A. Daas
https://arxiv.org/abs/2506.08865 htt…

Congruence conditions for the mod $λ$ values of the Fourier coefficients of classical eigenforms
We classify all instances of the condition $a_{p}(f) \equiv x \bmod λ$ being related to a congruence on the prime $p$, where $a_{p}(f)$ denotes the $p$th Fourier coefficient of a classical normalised cuspidal eigenform $f$ and $λ$ is a prime in the number field generated by the Fourier coefficients of $f$. This classification is done in terms of the (projective) image of the mod $λ$ Galois representation associated with $f$ and extends work by Swinnerton-Dyer. We highlight that for $x = 0$, …