Tootfinder

Exactly solvable Schr\"odinger operators related to the hypergeometric equation
Jan Derezi\'nski, Pedram Karimi
https://arxiv.org/abs/2509.03235 https://

Exactly solvable Schrödinger operators related to the hypergeometric equation
We study one-dimensional Schrödinger operators defined as closed operators that are exactly solvable in terms of the Gauss hypergeometric function. We allow the potentials to be complex. These operators fall into three groups. The first group can be reduced to the Gegenbauer equation, up to an affine transformation, a special case of the hypergeometric equation. The two other groups, which we call {\em hypergeometric of the first}, resp. {\em second kind}, can be reduced to the general Gauss…

Some Maker-Breaker games on hypergraphs
Patrick Bennett, Alan Frieze, Wesley Pegden
https://arxiv.org/abs/2509.02788 https://arxiv.org/pdf/2509.02788

Some Maker-Breaker games on hypergraphs
We consider some biased Maker-Breaker games. Starting with the complete $k$-uniform hypergraph on $n$ vertices, at each turn Maker claims one edge, and then Breaker claims $b$ edges. Maker's goal is to obtain a set of edges having some increasing property. We consider the case where Maker's desired property is minimum degree $m$, or having a full-rank incidence matrix, or having a Berge Hamilton cycle or having a perfect matching or a Hamilton $\ell$-cycle.

Generalized hypergeometric equations and $2$d TQFT for dormant opers in characteristic $\leq 7$
Keita Mori, Yasuhiro Wakabayashi
https://arxiv.org/abs/2509.03994 https://…

Generalized hypergeometric equations and $2$d TQFT for dormant opers in characteristic $\leq 7$
This note studies $\mathrm{PGL}_n$-opers arising from generalized hypergeometric differential equations in prime characteristic $p$. We prove that these opers are rigid within the class of dormant opers. By combining this rigidity result with previous work in the enumerative geometry of dormant opers, we obtain a complete and explicit description of the $2$d TQFTs that compute the number of dormant $\mathrm{PGL}_n$-opers for primes $p \leq 7$.

Mit mehreren Millionen km/h: Weiße Zwerge können einander aus Galaxie schleudern
Nachdem mehrere hyperschnelle Weiße Zwergsterne entdeckt wurden, gibt es nun eine Erklärung. Die Objekte sind das Produkt einer doppelten Sternenexplosion.

Barclays: hyperscalers have announced a total of 46 GW of AI data center capacity, which at full utilization will consume as much energy as ~44.2M US households (Robin Wigglesworth/Financial Times)
https://on.ft.com/4qCvVap

🇺🇦 Auf radioeins läuft...
Big Fox:
🎵 Final Call
#NowPlaying #BigFox
https://hybrisrec.bandcamp.com/track/final-call
https://open.spotify.com/track/1DgNqPoFcp5BGCMQiR9HqV

#openalt A great start to the day with a #peertube talk. If you wish to support the Czech instance, see the screens. @…

heise | Reale Ort in VR-Umgebungen verwandeln: "Meta Hyperscape" für Quest 3 im Test
Mit "Meta Hyperscape" lassen sich aus echten Räumen fotorealistische VR-Umgebungen erschaffen. Wir haben das in Innenräumen und im Freien ausprobiert.

Sources: Deutsche Bank is exploring ways to hedge its exposure to data centres after extending billions of dollars in debt to hyperscalers like Alphabet (Financial Times)
https://www.ft.com/content/c0428010-1373-463e-91e6-8fe7d64a26df

A High-Dimensional Extension of Wagner's Theorem and the Geometrization of Hypergraphs
Qiming Fang, Sihong Shao
https://arxiv.org/abs/2510.01926 https://

A High-Dimensional Extension of Wagner's Theorem and the Geometrization of Hypergraphs
This paper introduces a geometric representation of hypergraphs by representing hyperedges as simplices. Building on this framework, we employ homotopy groups to analyze the topological structure of hypergraphs embedded in high-dimensional Euclidean spaces. Leveraging this foundation, we extend Wagner's theorem to $\mathbb{R}^d$. Specifically, we establish that a triangulated $d$-uniform topological hypergraph embeds into $\mathbb{R}^d$ if and only if it contains neither $K_{d+3}^d$ nor $K_{3,d…