Clay weekly context brief for the Maths category (ISO week 2026-W43).

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. Jacobi Endpoint Pencils and Sharp Interlacing for Centered Binomial Samples
   Source: math.CV (Complex Variables)
   Link: https://arxiv.org/abs/2608.08714
   We study interlacing between real polynomial quotients obtained from centered binomial samples of a fixed even or odd real entire function at consecutive odd degrees.
2. Quantitative Volume Estimate on Singular Sets of One-phase Free Boundary Problems in Ricci Limit Spaces
   Source: math.DG (Differential Geometry)
   Link: https://arxiv.org/abs/2610.20986
   We study limit solutions of the one-phase free boundary problem on noncollapsed Ricci limit spaces.
3. Conditional limit laws for open intermittent dynamics
   Source: math.DS (Dynamical Systems)
   Link: https://arxiv.org/abs/2610.21175
   We obtain conditional limit theorems for open intermittent Liverani-Saussol-Vaienti (LSV) maps.
4. Stationarity equations for fractional affine area measures: ellipsoid rigidity and polytopal solutions
   Source: math.FA (Functional Analysis)
   Link: https://arxiv.org/abs/2610.21024
   Xi and Zhao established a first variation formula for affine inequalities involving radial mean bodies, and asked two geometric questions about the resulting stationarity equation: whether the bodies already known to satisfy it are the only ones, and whether its smooth solutions are exactly the ellipsoids.
5. A non-sober core-compact meet-continuous dcpo
   Source: math.GN (General Topology)
   Link: https://arxiv.org/abs/2610.22033
   We construct a meet-continuous dcpo whose Scott space is core-compact but neither sober nor locally compact.
6. Quadratic fields of values of finite solvable groups
   Source: math.GR (Group Theory)
   Link: https://arxiv.org/abs/2610.20992
   We show that if $G$ is a finite solvable group such that $E = \mathbb Q(\{\chi(g)\, |\, \chi\in{\rm Irr}(G),\ g \in G\})$ is an extension of degree 2 over the rationals, then $E = \mathbb Q(\sqrt{\pm d})$ for a positive integer $d$ all of whose prime divisors lie in $\{2, 3, 5\}$.
7. Exotic diffeomorphisms on closed aspherical $4$-manifolds
   Source: math.GT (Geometric Topology)
   Link: https://arxiv.org/abs/2610.21083
   We study a class of diffeomorphisms of closed manifolds obtained from Davis' reflection trick construction, which are obtained by reflecting a diffeomorphism supported in the fundamental chamber of such a manifold.
8. LWM-TF: A Wireless Foundation Model on 5G NR Time-Frequency Resource Grids
   Source: math.IT (Information Theory)
   Link: https://arxiv.org/abs/2610.21013
   Received OFDM grids preserve both pilot and payload observations, yet wireless foundation models are rarely pre-trained on them.
9. Local definable $(p,q)$-theorem and a refinement
   Source: math.LO (Logic)
   Link: https://arxiv.org/abs/2610.21738
   We prove the definable $(p,q)$-conjecture for NIP formulas in arbitrary first-order theories. We also prove a refinement and apply it to dense pairs.
10. On the Solution Sets of the Cone-Volume Map
   Source: math.MG (Metric Geometry)
   Link: https://arxiv.org/abs/2610.21533
   For a fixed set $U=(u_1,\ldots,u_m)$ of outer unit normals, we consider the cone-volume map which associates to a vector of support numbers $b\in\mathbb R^m_{> 0}$ the cone-volume vector $\gamma\in\mathbb R^m$ of the polytope \[ P(U,b)=\{x\in\mathbb{R}^n:U^\top x\leq b\}.
11. Poisson statistics for one-dimensional Anderson--Bernoulli Schr\"odinger operators
   Source: math-ph (Mathematical Physics)
   Link: https://arxiv.org/abs/2610.21268
   We prove Poisson local eigenvalue statistics for one-dimensional Schr\"odinger operators with nondegenerate Bernoulli potentials at any fixed nonzero coupling.
12. Galerkin finite element method for time fractional diffusion-wave equations with constant time delay
   Source: math.NA (Numerical Analysis)
   Link: https://arxiv.org/abs/2610.21056
   This paper studies numerical methods for the time fractional diffusion-wave equations with the constant delay.
13. Operator Algebraic Quantum Hypergroups
   Source: math.OA (Operator Algebras)
   Link: https://arxiv.org/abs/2610.21010
   We develop a theory of operator algebraic quantum hypergroups and their representations, formulated using a special case of the algebraic quantum hypergroup framework of van Daele and Delvaux.
14. Learning Warm Starts for the Simplex Method from Measured Solver Cost
   Source: math.OC (Optimization and Control)
   Link: https://arxiv.org/abs/2610.20892
   Learned warm starts for the simplex method build starting bases using predictions of which variables will be basic at optimality.
15. Third-moment cancellation and predictable representation in finite-state BSDE approximation
   Source: math.PR (Probability)
   Link: https://arxiv.org/abs/2610.20880
   We study finite-state approximations of Brownian-driven Markovian backward stochastic differential equations when the same one-step increment is used both for weak propagation and for martingale representation.
16. Characterizations in terms of Generalized Inverses
   Source: math.RA (Rings and Algebras)
   Link: https://arxiv.org/abs/2610.20760
   Using simply outer inverse and their differences, we characterize many known classes of rings including von Neumann regular, unit-regular, exchange, clean, and strongly clean rings.
17. A Proof of the Jung-Kim Conjecture on the Centers of Walled Brauer Algebras
   Source: math.RT (Representation Theory)
   Link: https://arxiv.org/abs/2610.21576
   We give a unified account of the five families of Khovanov arc algebras $K_n^m$, $K_n^{-\infty}$, $K_n^{+\infty}$, $K_n^\infty$ and $K_\infty^\infty$ in the framework of level-two tensor product categorifications, making explicit a perspective familiar to specialists.
18. Holomorphy rings and the Nullstellensatz over large fields
   Source: math.AC (Commutative Algebra)
   Link: https://arxiv.org/abs/2610.21039
   For an infinite field $K$ and an ideal $I\subseteq K[X_1,\dots,X_n]$, let $J(Z_K(I))$ be the ideal of polynomials vanishing on the $K$-rational zero locus of $I$.
19. Linear Independence of Polynomial Compositions with Bounded Input Degree
   Source: math.AG (Algebraic Geometry)
   Link: https://arxiv.org/abs/2610.20825
   We prove the weak composition-independence conjectures of Kohn, Marchetti, Massarenti and Mella.
20. $L^\infty$-regularity thresholds for a generalized Gross-Pitaevskii equation: dispersive blow-up vs. nonlinear stability
   Source: math.AP (Analysis of PDEs)
   Link: https://arxiv.org/abs/2610.20888
   We study a generalized Gross-Pitaevskii equation arising in the mean-field description of exciton-polariton Bose-Einstein condensates.
21. Non-simply connected Poincar\'e surgery
   Source: math.AT (Algebraic Topology)
   Link: https://arxiv.org/abs/2610.21100
   We give homotopy-theoretic proofs of the principal results of non-simply connected Poincar\'e surgery.
22. The $(n-1)$-linear restriction estimate in $\mathbb{R}^n$ with degenerate curvature
   Source: math.CA (Classical Analysis and ODEs)
   Link: https://arxiv.org/abs/2610.20909
   We revisit the $(n-1)$-linear restriction estimate in $\mathbb{R}^n$ proved by the first author in \cite{Be-6} and refine the result in the case when the curvature assumptions contain small parameters.
23. The $A^A$ problem for finite ordered sets
   Source: math.CO (Combinatorics)
   Link: https://arxiv.org/abs/2610.20817
   For ordered sets $X$ and $Y$, let $Y^X$ denote the ordered set of order-preserving maps from $X$ to $Y$, ordered pointwise.
24. A Krause-type recollement for Q-shaped derived categories
   Source: math.CT (Category Theory)
   Link: https://arxiv.org/abs/2610.21507
   Let k be a commutative noetherian hereditary ring and let Q be a small, Hom-finite, locally bounded k-linear category admitting a Serre functor and satisfying the strong retraction property, with nilpotent pseudo-radical.
25. Local-to-global maximality for plurisubharmonic functions with locally analytic singularities
   Source: math.CV (Complex Variables)
   Link: https://arxiv.org/abs/2610.05937
   We prove that a locally maximal plurisubharmonic function on a domain in $\bC^n$, $n\geq2$, is maximal if it has locally analytic singularities with a two-sided locally bounded remainder.
26. Infinitely many closed geodesic images on simply connected compact rank-one symmetric spaces
   Source: math.DG (Differential Geometry)
   Link: https://arxiv.org/abs/2610.21054
   We prove that every smooth Riemannian metric on the underlying smooth manifold of a simply connected compact rank-one symmetric space, namely $S^n$ $(n\ge2)$, $\CP^m$ $(m\ge1)$, $\HP^m$ $(m\ge1)$, or $\OP^2$ admits infinitely many geometrically distinct prime closed geodesics.
27. Semisimplicity and Rigidity of the Kontsevich--Zorich Cocycle for Products of Strata
   Source: math.DS (Dynamical Systems)
   Link: https://arxiv.org/abs/2610.21247
   We study the Kontsevich--Zorich cocycle, its fixed tensor constructions, and their finite direct sums over products of strata of Abelian differentials.
28. The best Ulam constant of the n-th order linear differential operator with constant coefficients
   Source: math.FA (Functional Analysis)
   Link: https://arxiv.org/abs/2610.21122
   Let $X$ be a Banach space over the field $\mathbb{K} \in \{\mathbb{R}, \mathbb{C}\}$, and let $L:\mathcal{C}^{n}(\mathbb{R},X)\to\mathcal{C}(\mathbb{R},X)$ be the $n$-th order linear differential operator defined by $Ly := y^{(n)} + a_1 y^{(n-1)} + \cdots + a_n y$, where $a_1,\ldots,a_n \in \mathbb{K}$ are fixed scalars and $n$ is a fixed positive integer.
29. Automorphisms of twisted Chevalley groups of type ${}^2E_6$ over local rings
   Source: math.GR (Group Theory)
   Link: https://arxiv.org/abs/2610.20994
   We classify abstract automorphisms of the elementary and full twisted Chevalley groups of type ${}^2E_6$ over commutative local rings with involution and $2$ invertible, for both isogeny types.
30. Holomorphic Triangles in the Heegaard Floer Pillowcase
   Source: math.GT (Geometric Topology)
   Link: https://arxiv.org/abs/2610.21153
   The Heegaard Floer pillowcase is a recurring local model for rational tangle replacement and exact-triangle constructions.
31. Superfast Spectral Compressed Sensing with Quadratic Convergence
   Source: math.IT (Information Theory)
   Link: https://arxiv.org/abs/2610.21068
   In this paper, we study the spectral compressed sensing problem of recovering a spectrally sparse signal from linear compressive measurements.

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.CO (Combinatorics); math.CT (Category Theory); math.CV (Complex Variables); math.DG (Differential Geometry); math.DS (Dynamical Systems); math.FA (Functional Analysis); math.GN (General Topology); math.GR (Group Theory); math.GT (Geometric Topology); math.IT (Information Theory); math.LO (Logic); math.MG (Metric Geometry); math.NA (Numerical Analysis); math.OA (Operator Algebras); math.OC (Optimization and Control); math.PR (Probability); math.RA (Rings and Algebras); math.RT (Representation Theory).
Selected 31 of 387 available items for this weekly brief.