Clay weekly context brief for the Maths category (ISO week 2026-W46). Clay tracks publications from the Maths feed list. Below are recent items from this category, each with its source and a short description of what the publication covers when one is available in the source feed. Recent publications: 1. Structure of derived Hecke algebras with coefficients in torsion-free profinite rings Source: math.RT (Representation Theory) Link: https://arxiv.org/abs/2609.34589 In this article, we study derived Hecke algebras with coefficients in torsion-free profinite rings regarded as discrete rings. 2. Fluctuation Correction and Global Solutions for the Stochastic Shigesada-Kawasaki-Teramoto System via Entropy-Based Regularization Source: math.PR (Probability) Link: https://arxiv.org/abs/2501.17953 We study a stochastic extension of the n-species Shigesada-Kawasaki-Teramoto (SKT) cross-diffusion system, in which a multiplicative noise term accounts for fluctuation corrections to the mean-field dynamics arising from a finite underlying population. 3. Entropic Martingale Optimal Transport with Wasserstein Relaxed Marginal Constraints Source: math.OC (Optimization and Control) Link: https://arxiv.org/abs/2611.08743 Martingale optimal transport (MOT) is a fundamental framework in robust finance, yet its stability under marginal perturbation no longer holds in high dimensions $d\geq 2$. 4. Weakly Unitary Zeon Matrices Source: math.OA (Operator Algebras) Link: https://arxiv.org/abs/2610.33891 In this paper, zeon matrix groups are discussed for the first time. 5. SparseModesNet for coupled thermal-hydraulic-mechanical system in heterogeneous porous media Source: math.NA (Numerical Analysis) Link: https://arxiv.org/abs/2611.09616 Coupled thermo-hydro-mechanical (THM) models describe interactions among displacement, fluid pressure, and temperature in geothermal systems. 6. Mode interaction in inclined-layer convection: a physical interpretation Source: math-ph (Mathematical Physics) Link: https://arxiv.org/abs/2611.09545 We carry out a numerical investigation of the Oberbeck--Boussinesq equations in a fluid layer inclined against gravity. 7. Landscape Analysis of Simultaneous Blind Deconvolution and Phase Retrieval via Structured Low-Rank Tensor Recovery Source: math.IT (Information Theory) Link: https://arxiv.org/abs/2509.10834 This paper studies the landscape of the simultaneous blind deconvolution and phase retrieval (BDPR) problem via a structured low-rank tensor recovery framework. 8. Chromatic Spherical and Renormalized Reshetikhin-Turaev Invariants for Drinfeld Centers Source: math.GT (Geometric Topology) Link: https://arxiv.org/abs/2611.06708 We give invariants of pairs $(M,\Gamma)$ consisting of a closed connected oriented three-manifold and an oriented framed ribbon graph embedded in $M$ colored by the Drinfeld center of a unimodular finite chromatic category $\mathcal C$. 9. Scl in graphs of groups Source: math.GR (Group Theory) Link: https://arxiv.org/abs/1904.08360 Let G be a group acting on a tree with cyclic edge and vertex stabilizers. 10. Topological Mundici Adjunction and Its Applications Source: math.GN (General Topology) Link: https://arxiv.org/abs/2611.09608 We establish a canonical topological lifting of Mundici equivalence, representing every topological MV-algebra as the unit interval of a topological $\ell$-group and extending the correspondence to a categorical adjunction. 11. On a characterization of spaces satisfying open mapping and equivalent theorems Source: math.FA (Functional Analysis) Link: https://arxiv.org/abs/1901.05899 We study open-mapping, continuous-inverse and closed-graph properties for maps whose domain and range belong to the same class of Hausdorff topological vector spaces. 12. Total Mean Curvature Gaps for Scalar-Flat Hypersurfaces Source: math.DG (Differential Geometry) Link: https://arxiv.org/abs/2610.24653 We prove that a complete connected scalar-flat Euclidean hypersurface of dimension $n\geq3$ is an affine hyperplane if its normalized mean curvature has sufficiently small $L^n$ norm. 13. On the Hodge Extension of Local K\"ahler Forms Source: math.CV (Complex Variables) Link: https://arxiv.org/abs/2610.38055 Let $X$ be a Stein manifold, and let $K=\{h\le0\}$ be a compact sublevel set of a strictly plurisubharmonic function $h$ defined near $K$. 14. Comparison categories: the normal form and the regularity of comparison data Source: math.CT (Category Theory) Link: https://arxiv.org/abs/2610.38143 Many equivalence relations of mathematics (Green's relations on a semigroup, orbit relations of group actions, ``same value of an invariant'') are defined by allowed transformations, of a morphism on its two sides or of a point of a set. 15. Multiplicity-Weighted Moments of a Two-Monomial Harmonic Map Beyond the Caustic Source: math.CA (Classical Analysis and ODEs) Link: https://arxiv.org/abs/2609.28370 While the Jacobian of a planar harmonic mapping keeps a constant sign, the signed and the unsigned area elements agree up to that sign, and the two natural moment hierarchies coincide. 16. Smooth atlas stratified spaces, K-Homology Orientations, and Gysin maps, Part 1 Source: math.AT (Algebraic Topology) Link: https://arxiv.org/abs/2505.14952 We introduce smooth atlas stratified spaces. 17. Well-posedness of weak solutions for the time-dependent thermal-fluid-solid multiphysical coupled model Source: math.AP (Analysis of PDEs) Link: https://arxiv.org/abs/2611.09482 This paper constructs a time-dependent thermal-fluid-solid multiphysical coupled model describing the interaction between a free fluid and a thermo-poroelastic medium and provides a rigorous mathematical analysis. 18. Geometric Detection and Finiteness of Log Crystalline Local Systems Source: math.AG (Algebraic Geometry) Link: https://arxiv.org/abs/2609.26318 We prove a geometric detection theorem for log crystalline local systems in the smooth proper setting with a normal crossings boundary. 19. Topological insights into Monoids and Module systems Source: math.AC (Commutative Algebra) Link: https://arxiv.org/abs/2603.08103 Let $H$ be a monoid and let $G$ denote its quotient groupoid. 20. Incidence algebras and beyond: brick-continuity and generic bricks Source: math.RT (Representation Theory) Link: https://arxiv.org/abs/2607.25443 We will show that the twelve families of minimally representation-infinite incidence algebras are brick-continuous and admit a generic brick, which will be explicitly constructed. 21. Line crossing problem for biased monotonic random walks in the plane Source: math.PR (Probability) Link: https://arxiv.org/abs/0709.3316 A $\beta$-biased monotonic random walk in the plane moves from $(x,y)$ to $(x+1,y)$ or $(x,y+1)$ with probabilities $1/(\beta+1)$ and $\beta/(\beta+1)$. 22. Drift-admissibility via Optimal Transport Source: math.OC (Optimization and Control) Link: https://arxiv.org/abs/2611.08505 We introduce structure-aware optimal transport diagnostics for assessing whether empirical time-series dynamics are compatible with a prescribed predictable-drift class. 23. A family of matrix flows converging to normal matrices Source: math.OA (Operator Algebras) Link: https://arxiv.org/abs/2602.11837 The celebrated Antezana-Pujals-Stojanoff Theorem states that the iterated Aluthge transforms of an arbitrary matrix converge to a normal matrix. 24. A Hybrid Quantum-Classical Coarse-to-Fine Finite Element Solver for Heterogeneous Darcy Flow Source: math.NA (Numerical Analysis) Link: https://arxiv.org/abs/2611.09593 Quantum linear system algorithms offer theoretical potential for solving large sparse systems from PDE discretizations. 25. Singular Vortex in the Large Deviation of Empirical Current for Symmetric Simple Exclusion Process Source: math-ph (Mathematical Physics) Link: https://arxiv.org/abs/2611.09526 We prove a large deviation estimate for singular current observables of the two-dimensional symmetric simple exclusion process. 26. From Formulation to Articulation: Considerations for AI-Assisted Research in Information Theory Source: math.IT (Information Theory) Link: https://arxiv.org/abs/2610.25490 Recent advances in artificial intelligence have contributed to several information-theoretic results through genuinely different modes: a language model may suggest a proof, participate in an extended mathematical dialogue, coordinate computation, or operate as one component of a search harness. 27. The proper geometric dimension of the mapping class groups of non-orientable surfaces with punctures Source: math.GT (Geometric Topology) Link: https://arxiv.org/abs/2609.22505 We study the proper geometric dimension of {\it full} mapping class groups of non-orientable surfaces with punctures. 28. Corrigendum to "Transitive permutation groups with trivial four point stabilizers" Source: math.GR (Group Theory) Link: https://arxiv.org/abs/2607.10710 This article revisits earlier work by the last author together with Kay Magaard. We correct mistakes in results about the Sylow 2- and 3-structure of groups that act with fixity 3 and one result about possible components, we improve some results and we add details. Sources in this brief: math-ph (Mathematical Physics); math.AC (Commutative Algebra); math.AG (Algebraic Geometry); math.AP (Analysis of PDEs); math.AT (Algebraic Topology); math.CA (Classical Analysis and ODEs); math.CT (Category Theory); math.CV (Complex Variables); math.DG (Differential Geometry); math.FA (Functional Analysis); math.GN (General Topology); math.GR (Group Theory); math.GT (Geometric Topology); math.IT (Information Theory); math.NA (Numerical Analysis); math.OA (Operator Algebras); math.OC (Optimization and Control); math.PR (Probability); math.RT (Representation Theory). Selected 28 of 266 available items for this weekly brief.