Tootfinder

Metaview, which builds AI tools to automate hiring, including interview note-taking and generating job descriptions, raised a $35M Series B led by GV (Beatrice Nolan/Fortune)
https://fortune.com/2025/06/25/uber-palantir-alums…

Exclusive: Uber and Palantir alums raise $35M to disrupt corporate recruitment with AI
Metaview’s full suite of AI tools aims to streamline and enhance every stage of the hiring process.

Don't miss our Sylius meetup on June 26th!
Register now and secure your spot: #php

PHPUGMRN 03/25 (The Sylius Meetup), Thu, Jun 26, 2025, 7:00 PM | Meetup
**Agenda:** 19:00 CET - Intro 19:05 CET - Brille24 - Post Mortem, Max Pesch 19:50 CET - Break 20:00 CET - Sylius & Automation, let's dive in!, Jacques Bodin-Hullin 20:50 CE

Infinitely many elliptic curves over $\mathbb{Q}(i)$ with rank 2 and $j$-invariant 1728
Ben Savoie
https://arxiv.org/abs/2506.17605 https://

Infinitely many elliptic curves over $\mathbb{Q}(i)$ with rank 2 and $j$-invariant 1728
We prove that there exist infinitely many elliptic curves over $\mathbb{Q}(i)$ of the form $y^2 = x^3 - γ^2 x$, where $γ\in \mathbb{Z}[i]$, with rank 2. In addition, we prove that if $p$ and $q$ are rational twin primes with $p \equiv 5 \bmod 8$, then $y^2 = x^3 + p q x$ has rank 2 over $\mathbb{Q}(i)$. Lastly, we prove that if $p$ is a rational prime of the form $p = a^2 + b^4$ (of which there are infinitely many) and $p \not\equiv 1 \bmod 16$, then $y^2 = x^3 - p x$ has rank 2 over $\mathbb…

Pointwise-relatively-compact subgroups and trivial-weight-free representations
Alexandru Chirvasitu
https://arxiv.org/abs/2506.18861 https://

Pointwise-relatively-compact subgroups and trivial-weight-free representations
A pointwise-elliptic subset of a topological group is one whose elements all generate relatively-compact subgroups. A connected locally compact group has a dense pointwise-elliptic subgroup if and only if it is an extension by a compact normal subgroup of a semidirect product $\mathbb{L}\rtimes \mathbb{K}$ with connected, simply-connected Lie $\mathbb{L}$, compact Lie $\mathbb{K}$, with the commutator subgroup $\mathbb{K}'$ acting on the Lie algebra $Lie(\mathbb{L})$ with no trivial weights. Th…

$\mathbb{G}$-uniform weighted K-stability for models on klt varieties
Jiyuan Han, Yaxiong Liu
https://arxiv.org/abs/2506.18039 https://

$\mathbb{G}$-uniform weighted K-stability for models on klt varieties
In this paper, we make a generalization of the results in \cite{Li22a} to the singular and weighted setting. In particular, we show that on a polarized projective klt variety, the $\mathbb{G}$-uniform weighted K-stability for models implies the $\mathbb{G}$-coercivity of the weighted Mabuchi functional. In the toric case, we further show that the $(\mathbb{C}^{\times})^n$-uniform $(\mathrm{v},\mathrm{w}\cdot\ell_{\mathrm{ext}})$-weighted K-stability is preserved when perturbing the polarization…

Weird $\mathbb R$-Factorizable Groups
Evgenii Reznichenko, Ol'ga Sipacheva
https://arxiv.org/abs/2506.18733 https://arxiv.org/pdf…

Weird $\mathbb R$-Factorizable Groups
The problem of the existence of non-pseudo-$\aleph_1$-compact $\mathbb R$-factorizable groups is studied. It is proved that any such group is submetrizable and has weight larger than $ω_1$. Closely related results concerning the $\mathbb R$-factorizability of products of topological groups and spaces are also obtained (a product $X\times Y$ of topological spaces is said to be $\mathbb R$-factorizable if any continuous function $X\times Y\to \mathbb R$ factors through a product of maps from $X$…

Embedding $\mathrm{SL}(2,\mathbb{C})/\mathbb{Z}_2$ in Complex Riemannian Geometry
John. W. Moffat, Ethan. J. Thompson
https://arxiv.org/abs/2506.19158 http…

Embedding $\mathrm{SL}(2,\mathbb{C})/\mathbb{Z}_2$ in Complex Riemannian Geometry
We present a unified framework demonstrating how the spinor complex Lorentz group SL(2,C)/Z\_2 is realized as a canonical subgroup within a four-dimensional complex Riemannian manifold. Building on the complex, holomorphic metric extension and contour-integration regularization of classical singularities, we show that promoting the metric to a complex-valued tensor on a complex 4-fold enlarges the frame bundle to SO(4,C). Its spin double cover factorizes as a product of two independent SL(2,C) …

On the volume of K-semistable Fano manifolds
Chi Li, Minghao Miao
https://arxiv.org/abs/2506.17420 https://arxiv.org/pdf/2506.17420…

On the volume of K-semistable Fano manifolds
We prove that the volume of an $n$-dimensional K-semistable Fano manifold that is not $\mathbb{P}^n$ is at most $2n^n$. Moreover, the equality holds only if $X\cong \mathbb{P}^1\times \mathbb{P}^{n-1}$ or $X$ is a smooth quadric hypersurface $Q\subset \mathbb{P}^{n+1}$. Our proof is based on a new connection between K-semistability and minimal rational curves. More generally, we show that the volume of a K-semistable Fano manifold with a minimal rational curve of degree $d$ is bounded above by …

On Fermat's Last Theorem over the $\mathbb{Z}_3$-extension of $\mathbb{Q}$ and other fields
Luis Dieulefait, Franco Golfieri Madriaga
https://arxiv.org/abs/2507.16883

On Fermat's Last Theorem over the $\mathbb{Z}_3$-extension of $\mathbb{Q}$ and other fields
The main result of the present article is a proof of Fermat's Last Theorem for sufficiently large prime exponents $p$ with $p \equiv 2 \pmod{3}$ over certain number fields. A particular case of these fields are the maximal real subfields of the cyclotomic extensions $\mathbb{Q}(ζ_{3^n})$ for every $n$. Our strategy consists in combining the modular method with a generalization of an arithmetic result of Pomey to these fields.

Monogenic sextic trinomials $x^6 Ax^3 B$ and their Galois groups
Joshua Harrington, Lenny Jones
https://arxiv.org/abs/2507.17021 https://

Monogenic sextic trinomials $x^6+Ax^3+B$ and their Galois groups
Let $f(x)=x^6+Ax^3+B\in {\mathbb Z}[x]$, with $A\ne 0$, and suppose that $f(x)$ is irreducible over ${\mathbb Q}$. We define $f(x)$ to be {\em monogenic} if $\{1,θ,θ^2,θ^3,θ^4,θ^{5}\}$ is a basis for the ring of integers of ${\mathbb Q}(θ)$, where $f(θ)=0$. For each possible Galois group $G$ of $f(x)$ over ${\mathbb Q}$, we use a theorem of Jakhar, Khanduja and Sangwan to give explicit descriptions of all monogenic trinomials $f(x)$ having Galois group $G$. We also investigate when the…