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Asynchronous Nonlinear Sheaf Diffusion for Multi-Agent Coordination
Yichen Zhao, Tyler Hanks, Hans Riess, Samuel Cohen, Matthew Hale, James Fairbanks
https://arxiv.org/abs/2510.00270

Asynchronous Nonlinear Sheaf Diffusion for Multi-Agent Coordination
Cellular sheaves and sheaf Laplacians provide a far-reaching generalization of graphs and graph Laplacians, resulting in a wide array of applications ranging from machine learning to multi-agent control. In the context of multi-agent systems, so called coordination sheaves provide a unifying formalism that models heterogeneous agents and coordination goals over undirected communication topologies, and applying sheaf diffusion drives agents to achieve their coordination goals. Existing literatur…

Computing weighted sheaf cohomology using noncommutative differential modules
Michael K. Brown, Daniel Erman
https://arxiv.org/abs/2510.02131 https://arxiv…

Computing weighted sheaf cohomology using noncommutative differential modules
We describe a novel method for computing sheaf cohomology over weighted projective stacks using exterior algebra and differential module techniques, generalizing an algorithm due to Eisenbud-Floystad-Schreyer over projective space.

Deformation quantisation of exact shifted symplectic structures, with an application to vanishing cycles
J. P. Pridham
https://arxiv.org/abs/2511.07602 https://arxiv.org/pdf/2511.07602 https://arxiv.org/html/2511.07602
arXiv:2511.07602v1 Announce Type: new
Abstract: We extend the author's and CPTVV's correspondence between shifted symplectic and Poisson structures to establish a correspondence between exact shifted symplectic structures and non-degenerate shifted Poisson structures with formal derivation, a concept generalising constructions by De Wilde and Lecomte. Our formulation is sufficiently general to encompass derived algebraic, analytic and $\mathcal{C}^{\infty}$ stacks, as well as Lagrangians and non-commutative generalisations. We also show that non-degenerate shifted Poisson structures with formal derivation carry unique self-dual deformation quantisations in any setting where the latter can be formulated.
One application is that for (not necessarily exact) $0$-shifted symplectic structures in analytic and $\mathcal{C}^{\infty}$ settings, it follows that the author's earlier parametrisations of quantisations are in fact independent of any choice of associator, and generalise Fedosov's parametrisation of quantisations for classical manifolds.
Our main application is to complex $(-1)$-shifted symplectic structures, showing that our unique quantisation of the canonical exact structure, a sheaf of twisted $BD_0$-algebras with derivation, gives rise to BBDJS's perverse sheaf of vanishing cycles, equipped with its monodromy operator.
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Symplectic Singularities, Color Confinement, and the Quantum Dirac Sheaf
Sergio Cecotti
https://arxiv.org/abs/2509.24605 https://arxiv.org/pdf/2509.24605…

Symplectic Singularities, Color Confinement, and the Quantum Dirac Sheaf
A singularity $\mathbb{C}^{2r}/G$, with $G$ a split symplectic reflection group, may or may not be crepant. Then the total space $\mathscr{X}$ of the Donagi-Witten integrable system is crepant for some 4d $\mathcal{N}=2$ SCFT and non-crepant for others. Which physical mechanism controls the (dis)crepancy? Surprisingly, it is the detailed physics of color confinement (and its generalizations for non-Lagrangian QFT). A 4d $\mathcal{N}=2$ SCFT carries a Frobenius algebra $\mathcal{R}$, the quantum…

Cohomology of vector bundles on the moduli space of parabolic connections on $\mathbb{P}^1$ minus $5$ points
Yuki Matsubara
https://arxiv.org/abs/2510.12578 https://

Cohomology of vector bundles on the moduli space of parabolic connections on $\mathbb{P}^1$ minus $5$ points
We study the moduli space of parabolic connections of rank two on the complex projective line $\mathbb{P}^1$ minus five points with fixed spectral data. This paper aims to compute the cohomology of the structure sheaf and a certain vector bundle on this space. We use this computation to extend the results of Arinkin, which proved a specific Geometric Langlands Correspondence to the case where these connections have five simple poles on $\mathbb{P}^1$. Moreover, we give an explicit geometric des…

Curved Boolean Logic: A Contextual Generalization of Propositional Logic with Algorithmic Consequences
Maximilian R. P. von Liechtenstein
https://arxiv.org/abs/2510.04716 https:…

Curved Boolean Logic: A Contextual Generalization of Propositional Logic with Algorithmic Consequences
Curved Boolean Logic (CBL) generalizes propositional logic by allowing local truth assignments that do not extend to a single global valuation, analogous to curvature in geometry. We give equivalent sheaf and exclusivity-graph semantics and a context-aware proof calculus that is conservative in the flat limit. We formalize CBL-SAT and basic complexity (NP-complete in general) and present operational operators (CBL-AC and CBL-CONS) that prune contradictions earlier on classical hardware. We mode…

Computational Drug Repurposing for Alzheimer's Disease via Sheaf Theoretic Population-Scale Analysis of snRNA-seq Data
Sean Cottrell, Seungmin Yoon, Xiaoqi Wei, Alex Dickson, Guo-Wei Wei
https://arxiv.org/abs/2509.25417

Computational Drug Repurposing for Alzheimer's Disease via Sheaf Theoretic Population-Scale Analysis of snRNA-seq Data
Single-cell and single-nucleus RNA sequencing (scRNA-seq /snRNA-seq) are widely used to reveal heterogeneity in cells, showing a growing potential for precision and personalized medicine. Nonetheless, sustainable drug discovery must be based on a population-level understanding of molecular mechanisms, which calls for the population-scale analysis of scRNA-seq/snRNA-seq data. This work introduces a sequential target-drug selection model for drug repurposing against Alzheimer's Disease (AD) targe…

The Chevalley--Weil formula for finite group actions on higher dimensional compact complex manifolds
Wenfei Liu, Renjie Lyu
https://arxiv.org/abs/2510.10430 https://

The Chevalley--Weil formula for finite group actions on higher dimensional compact complex manifolds
Building on the Atiyah--Singer holomorphic Lefschetz fixed-point theorem, we define ramification modules associated to the fixed loci of a finite group acting on a compact complex manifold. This allows us to generalize the Chevalley--Weil formula for compact Riemann surfaces to higher dimensions. More precisely, let $G$ be a finite group acting on a compact complex manifold $X$, and let $\mathcal{E}$ be a $G$-equivariant locally free sheaf on $X$. Then, in the representation ring $R(G)_\mathbb{…

Classical BV cohomology of the $N=1$ spinning particle
Eugenia Boffo, Martin Cederwall
https://arxiv.org/abs/2510.00655 https://arxiv.org/pdf/2510.00655

Classical BV cohomology of the $N=1$ spinning particle
We show that the classical Batalin--Vilkovisky cohomology at negative ghost number of the spinning particle, observed in ref. arXiv:1511.02135, is removed by a Koszul--Tate resolution involving saturation of Grassmann odd variables. The model thus satisfies the axioms of Felder and Kazhdan. The AKSZ formulation of the resolved model is described. We reveal partial information on the resolution of the constrained phase space, which involves resolving the parity-shifted tangent sheaf of the light…

$C^0$-rigidity of Legendrians and coisotropics via sheaf quantization
Tomohiro Asano, Yuichi Ike, Christopher Kuo, Wenyuan Li
https://arxiv.org/abs/2510.01746 https://

$C^0$-rigidity of Legendrians and coisotropics via sheaf quantization
We prove that in the standard cosphere bundle, for any contact homeomorphism in the closure of the compactly supported contactomorphism group, when the image of a coisotropic submanifold (not necessarily properly embedded) is smooth, it is still coisotropic. Moreover, when contactomorphisms in the sequence are in the identity component and the image of a Legendrian is smooth, the Maslov data is preserved, and the category of sheaves with singular support on the Legendrian and the microstalk cor…

A Morse complex for the homology of vanishing cycles
Aleksander Doan, Juan Mu\~noz-Ech\'aniz
https://arxiv.org/abs/2509.20685 https://arxiv.org/pdf/250…

A Morse complex for the homology of vanishing cycles
We construct Morse homology groups associated with any regular function on a smooth complex algebraic variety, allowing singular and non-compact critical loci. These groups are generated by critical points of a certain large pertubation of the function, built from a normal crossing compactification of the variety. They are canonically isomorphic to the homology of vanishing cycles and -- in the absence of bifurcations at infinity -- recover the hypercohomology of the perverse sheaf of vanishing…

Noncommutative localizations and joint spectra of a contractive quantum plane
Anar Dosi
https://arxiv.org/abs/2509.23539 https://arxiv.org/pdf/2509.23539…

Noncommutative localizations and joint spectra of a contractive quantum plane
In the present paper we investigate the localizations in the sense of J. L. Taylor of the Arens-Michael-Fréchet algebras occurred within the formal geometry of a contractive q-plane. It turns out that all noncommutative Fréchet algebras obtained by the Fréchet sheaves of the formal geometry are indeed localizations. That topological homology property of the structure sheaf results in the key properties of Taylor and Putinar spectra of the Banach q-modules.

Logarithmic jets and the chiral de Rham complex of a pair
Emile Bouaziz
https://arxiv.org/abs/2510.04515 https://arxiv.org/pdf/2510.04515

Logarithmic jets and the chiral de Rham complex of a pair
To a smooth variety $X$ with simple normal crossings divisor $D$, we associate a sheaf of vertex algebras on $X$, denoted $Ω^{ch}_{X}(\operatorname{log}D)$, whose conformal weight $0$ subspace is the algebra $Ω_{X}(\operatorname{log}D)$ of forms with log poles along $D$. We prove various basic structural results about $Ω^{ch}_{X}(\operatorname{log}D)$. In particular, if $X^{*}=X\setminus D$ has a volume form then we show that $Ω^{ch}_{X}(\operatorname{log}D)$ admits a topological structure …

On a Dichotomy for Skyscraper Sheaves under the Bridgeland-King-Reid Equivalence
Boris Tsvelikhovskiy
https://arxiv.org/abs/2509.15825 https://arxiv.org/pd…

On a Dichotomy for Skyscraper Sheaves under the Bridgeland-King-Reid Equivalence
Let $G \subset SL_3(\mathbb{C})$ be a finite abelian subgroup, and let $Y = G\operatorname{-}\mathrm{Hilb}(\mathbb{C}^3)$ be the corresponding $G$-Hilbert scheme. Denote by $Ψ: D^b_G(\mathrm{Coh}(\mathbb{C}^3)) \to D^b(\mathrm{Coh}(Y))$ the Bridgeland--King--Reid derived equivalence. For a nontrivial character $χ$ of $G$, let $χ^!$ be the corresponding skyscraper sheaf supported at the origin. It is known that $Ψ(χ^!)$ is always a pure sheaf supported either in degree $0$ or in degree $-1$…

Trace of Frobenius on nearby cycles for a $\Gamma_1(p)$-local model
Giulio Marazza
https://arxiv.org/abs/2509.21204 https://arxiv.org/pdf/2509.21204…

Trace of Frobenius on nearby cycles for a $Γ_1(p)$-local model
We compute the trace of Frobenius on the sheaf of nearby cycles for the integral model of the Siegel modular variety with pro-p Iwahori level structure, constructed by Haines and Stroh, in the case of $\text{GSp}_4$. To this end, we make use of a semistable resolution of this model due to Shadrach. Finally, we compare our results with calculations made by Horn, confirming a conjecture of Haines and Kottwitz in this case.