Tootfinder

Here are my favourites from the National Portrait Gallery's Portrait Award 2025. It's a fantastic selection this year, and free to see as always.
#art #portraits #painting

The arithmetic rank of determinantal nullcones
Jack Jeffries, Vaibhav Pandey, Anurag K. Singh, Uli Walther
https://arxiv.org/abs/2509.20470 https://arxiv.o…

The arithmetic rank of determinantal nullcones
We compute the arithmetic rank of nullcone ideals arising from the classical actions of the symplectic group, the general linear group, and the orthogonal group. We use these arithmetic rank calculations to establish striking vanishing results on the local cohomology modules supported at these nullcone ideals. This is done by analyzing the integer torsion in the critical local cohomology modules. The vanishing theorems that we obtain are sharp in multiple ways.

Products of strictly hyperbolic conjugacy classes in symplectic groups
Klaus Nielsen
https://arxiv.org/abs/2509.26237 https://arxiv.org/pdf/2509.26237

Products of strictly hyperbolic conjugacy classes in symplectic groups
We call a conjugacy class of the symplectic group Sp$(2n, K)$ over a field $K$ strictly hyperbolic if its minimal polynomial is of the form $q(x) q^*(x)$, where the polynomial $q(x)$ is prime to its reciprocal $q^*(x) := x^n q(x^{-1})$. It is shown that the product of 2 cyclic, strictly hyperbolic conjugacy classes of Sp$(2n, K)$ contains all nonscalar elements of Sp$(2n, K)$. It follows that the projective symplectic group has a conjugacy class of covering number 2, i.e. PSp$(2n,K) = Ω^2$ for…

I wrote about Tex Mex gravy, the definitive sauce for cheese enchiladas.

Matrix $A_p$-weights relative to a pseudo-metric
Morten Nielsen
https://arxiv.org/abs/2510.02849 https://arxiv.org/pdf/2510.02849

Matrix $A_p$-weights relative to a pseudo-metric
Matrix weights satisfying a Muckenhoupt $A_p$-condition relative to a family of anisotropic balls in $\mathbb{R}^d$ defined by a pseudo-metric are studied. It is shown that such matrix weights satisfy a doubling condition and a reverse Hölder inequality. In the special case, where the pseudo-metric is homogeneous with respect to a one-parameter dilation group, the corresponding Muckenhoupt class is shows to satisfy an invariance property under composition with affine transformations generated …

Asymptotically exact solution of the non-Hermitian disordered interacting Hatano-Nelson chain
Val\'eria M. Mattiello, Victor L. Quito, Eduardo Miranda
https://arxiv.org/abs/2509.16309

Asymptotically exact solution of the non-Hermitian disordered interacting Hatano-Nelson chain
We present an asymptotically exact solution of a paradigmatic non-Hermitian model: the disordered interacting fermionic Hatano-Nelson model, or equivalently, the non-Hermitian spin-1/2 XXZ model. We use a renormalization group method suited for disordered systems and show that non-Hermitian couplings are relevant perturbations to the Hermitian model, which ultimately leads to a quantum-to-classical crossover. The ground state of the model consists of a collection of strongly coupled pairs of sp…

The warm outer layer of a Little Red Dot as the source of [Fe II] and collisional Balmer lines with scattering wings
Alberto Torralba, Jorryt Matthee, Gabriele Pezzulli, Rohan P. Naidu, Yuzo Ishikawa, Gabriel B. Brammer, Seok-Jun Chang, John Chisholm, Anna de Graaff, Francesco D'Eugenio, Claudia Di Cesare, Anna-Christina Eilers, Jenny E. Greene, Max Gronke, Edoardo Iani, Vasily Kokorev, Gauri Kotiwale, Ivan Kramarenko, Yilun Ma, Sara Mascia, Benjam\'in Navarrete, Erica Nelson, …

The warm outer layer of a Little Red Dot as the source of [Fe II] and collisional Balmer lines with scattering wings
The population of the Little Red Dots (LRDs) may represent a key phase of supermassive black hole (SMBH) growth. A cocoon of dense excited gas is emerging as key component to explain the most striking properties of LRDs, such as strong Balmer breaks and Balmer absorption, as well as the weak IR emission. To dissect the structure of LRDs, we analyze new deep JWST/NIRSpec PRISM and G395H spectra of FRESCO-GN-9771, one of the most luminous known LRDs at $z=5.5$. These reveal a strong Balmer break,…

When is Trump sending the national guard to New York City? I saw a guy in full WWII-era German military garb on the subway platform this morning.

More big cuts to Universities and Colleges in Canada/BC.
This time it's smaller colleges in the Interior of BC. Coast Mountain College in Prince Rupert/Northwest, and Selkirk College in the SE/Nelson.
The Hazelton campus of CMC is being closed as is the Fine Arts campus of Selkirk.
All because successive Provincial and Federal governments in Canada thought the gravy-train of International students would last forever, allowing them to redirect funding for Post Secondary to other parts of the budget.
I don't think the system has found the bottom yet, and at the end, it will be Domestic students who suffer most from hugely diminished services at their local, and regional, and national colleges and Universities.
#Education #CanPoli #CdnPoli #PostSecondary #Investment
edit: the article is by @…

https://www.cbc.ca/news/canada/british-columbia/coast-mountain-college-hazelton-closing-campus-cuts-9.6946111