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Hochschild Cohomology of Isotropic Grassmannians
Anton Fonarev
https://arxiv.org/abs/2506.09727 https://arxiv.org/pdf/2506.09727

Hochschild Cohomology of Isotropic Grassmannians
We prove that nonspecial isotropic Grassmannians (that is, all isotropic Grassmannians which are neither (co)adjoint nor (co)minuscule, except $\mathsf{OGr}(n-1, 2n+1)$ for $n\geq 4$), are not Hochschild global, thus establishing a conjecture by P. Belmans and M. Smirnov. As a corollary, we conclude that Bott vanishing fails for all these varieties.

Deformation of ellipsoidal droplets in homogeneous and isotropic turbulence
Fabio Guglietta, Diego Taglienti, Mauro Sbragaglia
https://arxiv.org/abs/2506.09692

Deformation of ellipsoidal droplets in homogeneous and isotropic turbulence
We study the statistics of deformation of neutrally buoyant droplets in homogeneous isotropic turbulence (HIT), wherein the characteristic droplet size $R$ is smaller than the characteristic Kolmogorov scale $η$ of the turbulent flow. We systematically focus on the characterization of droplet statistics obtained with various phenomenological ellipsoidal models (EMs) -- assuming that the droplet preserves the ellipsoidal shape at all times - with the droplet moving as a passive tracer in the tu…

This https://arxiv.org/abs/2011.02575 has been replaced.
link: https://scholar.google.com/scholar?q=a

The group of affine transformations of homogeneous spaces with discrete isotropy
We present a method to compute the group of affine transformations of a homogeneous $G$-space under specific conditions: when the group $G$ and the homogeneous $G$-space admit linear connections so that the natural projection is affine, and with discrete isotropy group. If $G$ admits a bi-invariant linear connection, we establish conditions under which the homogeneous space admits an invariant linear connection. As a consequence, when the isotropy group is discrete, their respective groups of a…

CMB line-of-sight integrators for nearly-isotropic cosmological models
Jo\~ao G. Vicente, Thiago S. Pereira, Cyril Pitrou
https://arxiv.org/abs/2506.07786 …

CMB line-of-sight integrators for nearly-isotropic cosmological models
Homogeneous and nearly-isotropic cosmological models are natural extensions of standard Friedmann cosmologies. Constraining their features is crucial, as any detection of their properties would impact our understanding of inflation and the cosmological principle. Since these models evolve as a set of non-interacting scalar, vector, and tensor modes on top of homogeneous and isotropic spacetimes, their imprints on cosmological observables, particularly the CMB, can be obtained using standard lin…

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This https://arxiv.org/abs/2406.16627 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A Random Integration Algorithm for High-dimensional Function Spaces
We introduce a novel random integration algorithm that boasts both high convergence order and polynomial tractability for functions characterized by sparse frequencies or rapidly decaying Fourier coefficients. Specifically, for integration in periodic isotropic Sobolev space and the isotropic Sobolev space with compact support, our approach attains a nearly optimal root mean square error (RMSE) bound. In contrast to previous nearly optimal algorithms, our method exhibits polynomial tractability…

Improved H2-He and H2-H2 Collision-Induced Absorption Models and Application to Outer-Planet Atmospheres
Glenn S. Orton, Magnus Gustafsson, Leigh N. Fletcher, Michael T. Roman, James A. Sinclair
https://arxiv.org/abs/2506.09257

Improved H2-He and H2-H2 Collision-Induced Absorption Models and Application to Outer-Planet Atmospheres
Using state-of-the-art ab initio interaction-induced dipole and potential-energy surfaces for hydrogen-helium (H2-He) pairs, we compute the rototranslational collision-induced absorption coefficient at 40-400 K for frequencies covering 0-4000 cm-1. The quantum mechanical scattering calculations account for the full anisotropic interaction potential, replacing the isotropic approximation. The absorption data are expected to be accurate with an uncertainty of 2% or better up to 2500 cm-1. The unc…

This https://arxiv.org/abs/2505.04760 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Isotropic Torsors on Smooth Algebras over Prüfer Rings
The Grothendieck--Serre conjecture predicts that every generically trivial torsor under a reductive group over a regular semilocal ring is itself trivial. Extending the work of Česnavičius and Fedorov, we prove a non-noetherian analogue of this conjecture for rings $A$ that are semilocalisations of smooth schemes over valuation rings of rank one, and for reductive $A$-group schemes $G$ that are totally isotropic. Roughly speaking, such group schemes are characterised by the existence of a par…

A note on isothermic coordinate system for spacelike surfaces with constant mean curvature in Lorentz-Minkowski space
Yu Kawakami, Kaito Satake
https://arxiv.org/abs/2506.07516

A note on isothermic coordinate system for spacelike surfaces with constant mean curvature in Lorentz-Minkowski space
In this note, we present an elementary proof of the existence of isothermic coordinate system and explore its application to global property for space-like surfaces with constant mean curvature in the Lorentz-Minkowski three-space.

Vector bundles on bielliptic surfaces: Ulrich bundles and degree of irrationality
Edoardo Mason
https://arxiv.org/abs/2506.10696 https://

Vector bundles on bielliptic surfaces: Ulrich bundles and degree of irrationality
This paper deals with two problems about vector bundles on bielliptic surfaces. The first is to give a classification of Ulrich bundles on such surfaces $S$, which depends on the topological type of $S$. In doing so, we study the weak Brill-Noether property for moduli spaces of sheaves with isotropic Mukai vector. Adapting an idea of Moretti, we also interpret the problem of determining the degree of irrationality of bielliptic surfaces in terms of the existence of certain stable vector bundles…