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$(d,\sigma)$-twisted Affine-Virasoro superalgebras
Rencai L\"u, Xizhou You, Kaiming Zhao
https://arxiv.org/abs/2507.00349 https://

$(d,σ)$-twisted Affine-Virasoro superalgebras
For any finite dimensional Lie superalgebra $\dot{\mathfrak{g}}$ (maybe a Lie algebra) with an even derivation $d$ and a finite order automorphism $σ$ that commutes with $d$, we introduce the $(d,σ)$-twisted Affine-Virasoro superalgebra $\mathfrak{L}=\mathfrak{L}(\dot{\mathfrak{g}},d,σ)$ and determine its universal central extension $\hat{\mathfrak{L}}=\hat{\mathfrak{L}}(\dot{\mathfrak{g}},d,σ)$. This is a huge class of infinite-dimensional Lie superalgebras. Such Lie superalgebras consist …

$L^2$-Hodge theory of Hybrid Landau-Ginzburg models of Calabi-Yau complete intersections
Jeehoon Park, Jaewon Yoo
https://arxiv.org/abs/2505.24218 https://…

$L^2$-Hodge theory of Hybrid Landau-Ginzburg models of Calabi-Yau complete intersections
Given a Calabi-Yau smooth projective complete intersection variety $V$ over $\C$, a hybrid Landau-Ginzburg (LG) model may be associated using the Cayley trick. This hybrid LG model comprises a non-compact Calabi-Yau manifold $X_{CY}$, and a holomorphic function $W$, defined on $X_{CY}$, such that the critical locus of $W$ is isomorphic to $V$. We construct a complete Kähler metric $\mathfrak{g}$ and a bounded Calabi-Yau volume form $Ω$ on $X_{CY}$ such that $(X_{CY},\mathfrak{g}, Ω)$ is a bo…

Shuffle algebras, lattice paths and quantum toroidal $\mathfrak{gl}_{n|m}$
Alexandr Garbali, Andrei Negu\c{t}
https://arxiv.org/abs/2507.00538 https://

Shuffle algebras, lattice paths and quantum toroidal $\mathfrak{gl}_{n|m}$
We describe and compute various families of commuting elements of the matrix shuffle algebra of type $\mathfrak{gl}_{n|m}$, which is expected to be isomorphic to quantum toroidal $\mathfrak{gl}_{n|m}$. Our formulas are given in terms of partial traces of products of $R$-matrices of the quantum affine algebra $U_t(\dot{\mathfrak{gl}}_{n|m})$, and have a lattice path interpretation. Our calculations are based on the machinery of the quantum toroidal algebras and a new anti-homomorp…

Rust's Stable MIR project is being slept on. It's pitched as a tool for formal verification, but it's more general than that. Once stabilized, it will almost be a stable compiler plugin API!
It doesn't just include what you get from `--emit=mir` (IR for each function), but also has full type and trait information, and will likely even support interactive queries like "does type implement trait”.
In short, it'll be perfect for metaprogramming!
[1/2]…

Using "AI" is no longer optional at Microsoft. Reminds me how when Meta had to force their engineers to use their "Metaverse" product.
If your product doesn't even gain traction internally, maybe it's just ... shit?
(Original title: ‘AI is no longer optional’ — Microsoft admits AI doesn’t help at work)

‘AI is no longer optional’ — Microsoft admits AI doesn’t help at work
An internal Microsoft memo has leaked. It was written by Julia Liuson, president of the Developer Division at Microsoft and GitHub. The memo tells managers to evaluate employees based on how much t…

Multivariable period rings of $p$-adic false Tate curve extension
Yijun Yuan
https://arxiv.org/abs/2505.24064 https://arxiv.org/pdf/2…

Multivariable period rings of $p$-adic false Tate curve extension
Let $p\geq 3$ be a prime number and $K$ be a finite extension of $\mathbf{Q}_p$ with uniformizer $π_K$. In this article, we introduce two multivariable period rings $\mathbf{A}_{\mathfrak{F},K}^{\operatorname{np}}$ and $\mathbf{A}_{\mathfrak{F},K}^{\operatorname{np},\operatorname{c}}$ for the étale $(φ,Γ_{\mathfrak{F},K})$-modules of $p$-adic false Tate curve extension $K\left(π_K^{1/p^\infty},ζ_{p^\infty}\right)$. Various properties of these rings are studied and as applications, we show…

A law of large numbers for kinetic interacting diffusions
Carlo Bellingeri, Fabio Coppini
https://arxiv.org/abs/2506.01769 https://ar…

A law of large numbers for kinetic interacting diffusions
We study the convergence of the empirical distribution associated with a system of interacting kinetic particles subject to independent Brownian forcing in a finite horizon setting, using some recent progress on kinetic non-linear partial differential equations. Under general assumptions that require only weak convergence on the initial datum -without assuming independence or moment conditions- we prove convergence in probability to the corresponding non-linear Fokker-Planck PDE.

"#Microsoft’s #AI tools don’t work. Microsoft AI doesn’t make you more effective. Microsoft AI won’t do the job better.
If it did, Microsoft staff would be using it already. The competition inside Microsoft is vicious. If AI would get them ahead of the other guy, they’d use it."
via…

This https://arxiv.org/abs/2402.08628 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Nonlinear Graphon mean-field systems
We address a system of weakly interacting particles where the heterogenous connections among the particles are described by a graph sequence and the number of particles grows to infinity. Our results extend the existing law of large numbers and propagation of chaos results to the case where the interaction between one particle and its neighbors is expressed as a nonlinear function of the local empirical measure. In the limit of the number of particles which tends to infinity, if the graph seque…

Paper-Scissors-Stone Model for Interacting Population and its Limit Theorem
Yasunori Okabe, Hajime Mano, Yoshiaki Itoh
https://arxiv.org/abs/2507.00362 htt…

Paper-Scissors-Stone Model for Interacting Population and its Limit Theorem
This paper treats a random collision model of three species, which is represented by the random time change of three standard Poisson processes. The prey-predator relation in the random collision model looks like paper-scissors-stone game, and the model is called the paper-scissors model. At first, we investigate the stochastic structure of our model. By using stochastic calculus, the model is decomposed into a semi-martingale, and we prove a weak law of large numbers and a central limit theore…