Tootfinder

1/2 “My input stream is full of it: Fear and loathing and cheerleading and prognosticating on what generative AI means and whether it’s Good or Bad and what we should be doing. All the channels: Blogs and peer-reviewed papers and social-media posts and business-news stories. So there’s lots of AI angst out there, but this is mine. I think the following is a bit unique because it focuses on cost, working backward from there.”

AI Angst

Special Cases of the Shafarevich Conjecture for Complete Intersections in Abelian Varieties
Frank Lu
https://arxiv.org/abs/2506.14935 https://

Special Cases of the Shafarevich Conjecture for Complete Intersections in Abelian Varieties
In this paper, we prove the Shafarevich conjecture for certain complete intersections of hypersurfaces in abelian varieties defined over a number field $K$ using the Lawrence-Venkatesh method. The main new inputs we need are computation of certain Euler characteristics of these complete intersections and a big monodromy statement for the variation of Hodge structure arising from the middle cohomology of a family of such complete intersections. Following \cite{ls25}, we prove the latter by relat…

Failure of Bott vanishing for (co)adjoint partial flag varieties
Pieter Belmans
https://arxiv.org/abs/2506.09811 https://arxiv.org/pd…

Failure of Bott vanishing for (co)adjoint partial flag varieties
Bott vanishing is a strong vanishing result for the cohomology of exterior powers of the cotangent bundle twisted by ample line bundles. Buch-Thomsen-Lauritzen-Mehta conjectured that partial flag varieties (which are not products of projective spaces) do not satisfy Bott vanishing, despite all their other nice properties. The cominuscule case is an easy application of the Borel-Weil-Bott theorem, following results of Snow. We show that the (co)adjoint partial flag varieties of all classical and…

Three-Dimensional Channel Modeling for Molecular Communications in Tubular Environments with Heterogeneous Boundary Conditions
Yun-Feng Lo, Changmin Lee, Chan-Byoung Chae
https://arxiv.org/abs/2506.00803

Three-Dimensional Channel Modeling for Molecular Communications in Tubular Environments with Heterogeneous Boundary Conditions
Molecular communication (MC), one of the emerging techniques in the field of communication, is entering a new phase following several decades of foundational research. Recently, attention has shifted toward MC in liquid media, particularly within tubular environments, due to novel application scenarios. The spatial constraints of such environments make accurate modeling of molecular movement in tubes more challenging than in traditional free-space channels. In this paper, we propose a three-dim…

Population Synthesis Study on the Binary Origin of Type Ibn Supernovae
Takatoshi Ko, Tomoya Kinugawa, Daichi Tsuna, Ryosuke Hirai, Yuki Takei
https://arxiv.org/abs/2506.00931

Population Synthesis Study on the Binary Origin of Type Ibn Supernovae
Type Ibn supernovae (SNe) are a class of SN explosions whose progenitors are surrounded by dense helium-rich circumstellar matter (CSM). Some models have been proposed for how to form the dense CSM, with promising scenarios involving either binaries with a low-mass ($\lesssim 3~M_\odot$) helium (He) star, or mergers following common envelope phases between a He star and a compact object. Using rapid binary population synthesis calculations, we estimate the event rate of these channels and compa…

Unwinding the rare $\Omega$ sector: Fragmentation of fully charmed baryons from HL-LHC to FCC
Francesco Giovanni Celiberto
https://arxiv.org/abs/2506.00776

Unwinding the rare $Ω$ sector: Fragmentation of fully charmed baryons from HL-LHC to FCC
By adopting a hadron-structure-oriented approach, we present and discuss the release of the novel OMG3Q1.0 set of collinear fragmentation functions for fully charmed, rare $Ω$ baryons. Our methodology combines diquark-like proxy model inputs for both charm-quark and gluon channels, calculated at the initial energy scales, with a DGLAP evolution that ensures a consistent treatment of heavy-quark thresholds, following directly from the HF-NRevo scheme. We complement our work with a phenomenologi…

This https://arxiv.org/abs/2501.04357 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Generators of top cohomology
Let $R$ be a commutative noetherian ring and $f: X \to \mathrm{Spec} R$ a proper smooth morphism, of relative dimension $n$. From Hartshorne, Residues and Duality, Springer, 1966, one knows that the trace map $\mathrm{Tr}_f : \mathrm{H}^n(X, ω_{X/R}) \to R$ is an isomorphism when $f$ has geometrically connected fibres. We construct an exact sequence that generates $\mathrm{Ext}_X^n(\mathcal{O}_X, ω_{X/R}) = \mathrm{H}^n(X, ω_{X/R})$ as an $R$-module in the following cases: (1) when $R$ is…