Tootfinder

Diophantine approximation on abelian varieties; a conjecture of M. Waldschmidt
Lior Fishman, David Lambert, Keith Merrill, David Simmons
https://arxiv.org/abs/2506.19060

Diophantine approximation on abelian varieties; a conjecture of M. Waldschmidt
Following the work of Waldschmidt, we investigate problems in Diophantine approximation on abelian varieties. First we show that a conjecture of Waldschmidt for a given simple abelian variety is equivalent to a well-known Diophantine condition holding for a certain matrix related to that variety. We then posit a related but weaker conjecture, and establish the upper bound direction of that conjecture in full generality. For rank 1 elliptic curves defined over a number field $K \subset \mathbb{R…

Distinguishing Filling Invariants Associated to Conjugacy in Groups
Conan Gillis, Timothy Riley
https://arxiv.org/abs/2506.19264 https://

Distinguishing Filling Invariants Associated to Conjugacy in Groups
Brick and Corson introduced annular Dehn functions in 1998 to quantify the conjugacy problem for finitely generated groups and gave the fundamental relationships between it, the Dehn function, and the conjugator length function. We furnish the theory with diverse examples groups. In particular, we show that these three invariants are independent -- no two of the three functions determine the other.

Poster No 857: Plastic changes in the occipital regions during pitch perception associate with blindness onset age; "Specifically, the primary visual cortex remains engaged in pitch processing tasks following late blindness." https://doi.org/10.5281/zenodo.15641972

On Gy\'arf\'as' Path-Colour Problem
Ben Cameron, Alexander Clow
https://arxiv.org/abs/2506.19100 https://arxiv.org/pdf/25…

On Gyárfás' Path-Colour Problem
In their 1997 paper titled ``Fruit Salad", Gyárfás posed the following conjecture: there exists a constant $k$ such that if each path of a graph spans a $3$-colourable subgraph, then the graph is $k$-colourable. It is noted that $k=4$ might suffice. Let $r(G)$ be the maximum chromatic number of any subgraph $H$ of $G$ where $H$ is spanned by a path. The only progress on this conjecture comes from Randerath and Schiermeyer in 2002, who proved that if $G$ is an $n$ vertex graph, then $χ(G) \le…

The infinite dimensional geometry of conjugation invariant generating sets
Sabine Chu, George Domat, Christine Gao, Ananya Prasanna, Alex Wright
https://arxiv.org/abs/2506.18618

The infinite dimensional geometry of conjugation invariant generating sets
We consider a number of examples of groups together with an infinite conjugation invariant generating set, including: the free group with the generating set of all separable elements; surface groups with the generating set of all non-filling curves; mapping class groups and outer automorphism groups of free groups with the generating sets of all reducible elements; and groups with suitable actions on Gromov hyperbolic spaces with a generating set of elliptic elements. In these Cayley graphs we …

Binary Neutron Star Mergers as Potential Sources for Ultra-High-Energy Cosmic Rays and High-Energy Neutrinos
Gang Guo, Yong-Zhong Qian, Meng-Ru Wu
https://arxiv.org/abs/2506.17581

Binary Neutron Star Mergers as Potential Sources for Ultra-High-Energy Cosmic Rays and High-Energy Neutrinos
Recent studies suggest that the most energetic cosmic rays, exceeding 100 EeV, may primarily consist of $r$-process nuclei. This highlights binary neutron star mergers and collapsars as promising sources of ultra-high-energy cosmic rays (UHECRs). Building on these insights, we examine the conditions that facilitate the efficient production of UHE $r$-process nuclei during the prompt radiation (PR), extended emission (EE), and plateau emission phases of short gamma-ray bursts (sGRBs) following n…

An Ejection Event Captured by VLBI During the Outburst of Swift J1727.8$-$1613
Hongmin Cao, Jun Yang, S\'andor Frey, Callan M. Wood, James C. A. Miller-Jones, Krisztina \'E. Gab\'anyi, Giulia Migliori, Marcello Giroletti, Lang Cui, Tao An, Xiaoyu Hong, Weihua Wang
https://arxiv.org/abs/2506.18817

An Ejection Event Captured by VLBI During the Outburst of Swift J1727.8$-$1613
We observed a newly-discovered Galactic black hole X-ray binary Swift J1727.8$-$1613 with the European Very Long Baseline Interferometry Network (EVN) at 5 GHz. The observation was conducted immediately following a radio quenching event detected by the Karl G. Jansky Very Large Array (VLA). The visibility amplitude evolution over time reveals a large-amplitude radio flare and is consistent with an ejection event. The data can be interpreted either as a stationary component (i.e., the radio core…

Yeah, this is not surprising…
“Airlines and Trump Administration Backpedal on Protections for Travelers With Wheelchairs”
https://www.nytimes.com/2025/06/20/travel/wheelchair-flights-delta-united-american.html
Archive: …

Airlines Challenge Protections For Travelers With Wheelchairs
A landmark rule to expand the rights of disabled air travelers has been hamstrung by a lawsuit from major airlines and delayed enforcement by the Transportation Department.

Three different iOS Mastodon apps: Icecubes, Trunks, and the official, reference implementation. In addition to very different experiences and quirks, each show a noticeably different Home time line view. Order, missing toots, hashtag following, filter handling, etc.
A web browser and IceCubes seem to give the best, most consistent view I'd expect, but the scrolling bug in IceCubes makes it practically unusable for many.
:-(

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…