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Theta-invariants of $\mathbb{Z}\pi$-homology equivalences to spherical 3-manifolds
Hisatoshi Kodani, Tadayuki Watanabe
https://arxiv.org/abs/2507.12121 htt…

Theta-invariants of $\mathbb{Z}π$-homology equivalences to spherical 3-manifolds
We study Bott and Cattaneo's $Θ$-invariant of 3-manifolds applied to $\mathbb{Z}π$-homology equivalences from 3-manifolds to a fixed spherical 3-manifold. The $Θ$-invariants are defined by integrals over configuration spaces of two points with local systems and by choosing some invariant tensors. We compute upper bounds of the dimensions of the space spanned by the Bott--Cattaneo $Θ$-invariants and of that spanned by Garoufalidis and Levine's finite type invariants of type 2. The computatio…

Este nuevo prisma sobre la #IA no lo habíamos contemplado aún: el consumo de energía es tan alto que estš afectando en una subida de precios para todos los consumidores. Y ya sabemos que la subida de la luz repercute en la subida de todos los demšs precios.
Enhorabuena a los genios.
Edito para meter enlace

Coupled KPZ equations and their decoupleability
Boliang Fu, Tadahisa Funaki, Sunder Sethuraman, Shankar Venkataramani
https://arxiv.org/abs/2508.04637 https://

Coupled KPZ equations and their decoupleability
We discuss characterizations of the decoupleability, partial and full, of trilinear or completely symmetric real $n\times n\times n$ tensors, which inform on the structure of certain coupled KPZ equations. Informally, when the tensor is partially decoupleable, one of the components in the coupled KPZ equation splits off from the others, while when the tensor is fully decoupleable, each of the $n$ components splits off from the others. Such a characterization is recast as a problem of membersh…