Clay weekly context brief for the Maths category (ISO week 2026-W34).

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. The Noetherian Case of Bayart's Power-Series Question
   Source: math.AC (Commutative Algebra)
   Link: https://arxiv.org/abs/2608.12642
   Let $R$ be a commutative Noetherian ring.
2. Virasoro Recursions for Simplicially Stable Curves with Colliding Markings
   Source: math.AG (Algebraic Geometry)
   Link: https://arxiv.org/abs/2608.12507
   We study descendant integrals on moduli stacks of simplicially stable curves.
3. Spatial decay and nonlinear smoothing of the sixth-order Boussinesq equation
   Source: math.AP (Analysis of PDEs)
   Link: https://arxiv.org/abs/2608.12366
   In this paper, we study the initial value problem of the sixth-order Boussinesq equation with quadratic and cubic nonlinearities in arbitrary spatial dimensions.
4. The fusion-stable tom Dieck homomorphism
   Source: math.AT (Algebraic Topology)
   Link: https://arxiv.org/abs/2608.12499
   Tornehave and Yal\c{c}in proved that the tom Dieck homomorphism, which sends a virtual real representation to a unit of the Burnside ring, is surjective for any $p$-group $S$.
5. Conformal Dimension of Measures and Quasisymmetric Dimension Reduction
   Source: math.CA (Classical Analysis and ODEs)
   Link: https://arxiv.org/abs/2608.12873
   We prove that the conformal dimension of every locally finite Borel measure is either zero or infinite.
6. On the Total Regularity of Almost Mixed Moore Graphs
   Source: math.CO (Combinatorics)
   Link: https://arxiv.org/abs/2608.12425
   The degree/diameter problem asks for the largest order of a graph with a given diameter and maximum vertex degree.
7. A Canonical Positive Definite Kernel Associated with the $\xi$-Bergman Kernel
   Source: math.CV (Complex Variables)
   Link: https://arxiv.org/abs/2608.13193
   Let $\Omega \subset \mathbb{C}^{n}$ and $\xi \in \ell^{1}$.
8. Rigidity of stable spacelike capillary hypersurfaces in de Sitter and Minkowski spaces
   Source: math.DG (Differential Geometry)
   Link: https://arxiv.org/abs/2608.13115
   We prove a rigidity theorem for compact spacelike capillary hypersurfaces in de~Sitter and Minkowski spaces: volume-preserving stability forces total umbilicity when the support is a spacelike totally umbilical hypersurface of nonnegative intrinsic curvature.
9. Laminations and External Angles for Similarity Pairs
   Source: math.DS (Dynamical Systems)
   Link: https://arxiv.org/abs/2608.12774
   A {\em similarity pair} is the dynamical system in $\mathbb{C}$ generated by two maps $f:z \to sz-1$ and $g:z \to sz+1$ for $|s|<1$.
10. The mixed spectral problem for radial Schr\"{o}dinger operators and Paley-Wiener spaces
   Source: math.FA (Functional Analysis)
   Link: https://arxiv.org/abs/2608.12733
   The inverse spectral problem for the radial Schr\"{o}dinger operators on the finite interval is investigated.
11. "Phase Transition" in fractional differential equations
   Source: math.GM (General Mathematics)
   Link: https://arxiv.org/abs/2608.12402
   The basic result in the theory of linear ODEs is that the dimension of the fundamental set of linearly independent solutions is equal to the order of equation.
12. Axioms of Continuous Separation
   Source: math.GN (General Topology)
   Link: https://arxiv.org/abs/2608.13086
   For a $T_1$-space $X$, let $Cld(X)$ denote all its nonempty closed subsets and $T_4(X)=\{(F_1,F_2)\in Cld(X)^2:F_1\cap F_2=\emptyset\}$.
13. Components of the Divisibility Graph of Finite Groups of Lie Type in Defining Characteristic $2$
   Source: math.GR (Group Theory)
   Link: https://arxiv.org/abs/2608.12501
   We determine the connected components of the divisibility graph of several families of finite groups of Lie type in defining characteristic $2$, extending the result of Abdolghafourian, Iranmanesh, and Niemeyer (arXiv:1612.04410), who treated odd defining characteristic.
14. On the minimal diameter of finite covers
   Source: math.GT (Geometric Topology)
   Link: https://arxiv.org/abs/2608.12887
   We prove that every closed hyperbolic surface admits a sequence of finite covers with asymptotically optimal diameters.
15. Channel Estimation for OTFS Systems With Overspread Doppler Shifts
   Source: math.IT (Information Theory)
   Link: https://arxiv.org/abs/2608.12524
   In this paper, we consider an orthogonal time frequency space (OTFS) system in time-varying channels with overspread Doppler shifts, typically found in non-terrestrial multi-satellite links.
16. Schwartz spaces on L-monoids: non-Archimedean
   Source: math.RT (Representation Theory)
   Link: https://arxiv.org/abs/2607.28507
   We complete the Braverman-Kazhdan-Ng\^{o} program over non-Archimedean local fields assuming local Langlands conjecture for tempered representations and a natural assumption on the $\gamma$-factors of non-supercuspidal discrete series.
17. On the Cartan Graphs of Nichols Algebras over Coquasi-Hopf Algebras
   Source: math.QA (Quantum Algebra)
   Link: https://arxiv.org/abs/2607.05065
   Over an algebraically closed field of characteristic zero, let $H$ be a coquasi-Hopf algebra with bijective antipode, and let $M$ be a tuple of finite-dimensional simple Yetter--Drinfeld modules over $H$.
18. Topological complexity of spiked random polynomials and finite-rank spherical integrals
   Source: math.PR (Probability)
   Link: https://arxiv.org/abs/2312.12323
   We study the annealed complexity of Gaussian random homogeneous polynomials on the $(N-1)$-dimensional unit sphere in the presence of deterministic perturbations depending on fixed orthonormal vectors and external parameters.
19. A Complete Characterization of Cartan Inclusions of Finite Dimensional $C^*$-algebras
   Source: math.OA (Operator Algebras)
   Link: https://arxiv.org/abs/2608.11711
   We give a complete characterization of Cartan inclusions of finite dimensional $C^*$-algebras in terms of their inclusion matrices.
20. Intersective Polynomials and Universal Separation of Divosor Profiles
   Source: math.NT (Number Theory)
   Link: https://arxiv.org/abs/2608.13388
   We classify universal divisor-profile separation for coprime polynomial pairs of arbitrary degree and for all pairs of degree at most two.
21. Stochastic gradient with least-squares control variates
   Source: math.NA (Numerical Analysis)
   Link: https://arxiv.org/abs/2507.20981
   The stochastic gradient descent (SGD) method is a widely used approach for solving stochastic optimization problems, but its convergence is typically slow.
22. Local and quasilocal conservation laws of three-state IRF cellular automata and their quantum deformations
   Source: math-ph (Mathematical Physics)
   Link: https://arxiv.org/abs/2608.13080
   Using patch-matrix-product methods, we study two reversible three-state interaction-round-a-face cellular automata introduced by Klobas and Prosen [J.
23. Sturmian lattices and Aperiodic tile sets
   Source: math.MG (Metric Geometry)
   Link: https://arxiv.org/abs/2506.19362
   We give an explicit algorithm to construct aperiodic tile sets based on Sturmian words of quadratic slopes.
24. Classifying $^*$-homomorphisms I: Unital simple nuclear $C^*$-algebras
   Source: math.KT (K-Theory and Homology)
   Link: https://arxiv.org/abs/2307.06480
   We classify the unital embeddings of a unital separable nuclear $C^*$-algebra satisfying the universal coefficient theorem into a unital simple separable nuclear $C^*$-algebra that tensorially absorbs the Jiang--Su algebra.
25. The multiplicity sequence of monomial ideals
   Source: math.AC (Commutative Algebra)
   Link: https://arxiv.org/abs/2608.12731
   We give a convex-geometric formula for the multiplicity sequence of a monomial ideal in terms of mixed volumes of polytopes constructed from its Newton polyhedron.
26. Collision-Hull Compression for Homogeneous Keller Maps and a Forty-Variable Counterexample to Zhao's Vanishing Conjecture
   Source: math.AG (Algebraic Geometry)
   Link: https://arxiv.org/abs/2608.12543
   We formulate an elementary collision-generated compression principle for homogeneous Keller maps.
27. Stochastic Nonlinear Waves in all the Right Phases
   Source: math.AP (Analysis of PDEs)
   Link: https://arxiv.org/abs/2608.12369
   I present an overview of different phases used in the literature to describe the phase of travelling waves in reaction-diffusion equations.
28. On the sphere spectrum from the viewpoint of linear logic
   Source: math.AT (Algebraic Topology)
   Link: https://arxiv.org/abs/2608.13012
   In this note, we show the category of $\Gamma$-sets with the sphere spectrum, the smash product, and the substitution product gives rise to an isomix linearly distributive category, which is a categorical semantics of the multiplicative fragment of linear logic.
29. Parabolic BMO, Parabolic Muckenhoupt Classes, and Parabolic Reverse H\"older Classes with Time Lag
   Source: math.CA (Classical Analysis and ODEs)
   Link: https://arxiv.org/abs/2608.13307
   We prove that, for any given time lag $\gamma\in(0,1)$, \begin{itemize} \item the one-sided parabolic BMO space $\mathrm{BMO}^+(\gamma)$ coincides with the parabolic BMO space $\mathrm{PBMO}^-(\gamma)$, i. e.

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.CV (Complex Variables); math.DG (Differential Geometry); math.DS (Dynamical Systems); math.FA (Functional Analysis); math.GM (General Mathematics); math.GN (General Topology); math.GR (Group Theory); math.GT (Geometric Topology); math.IT (Information Theory); math.KT (K-Theory and Homology); math.MG (Metric Geometry); math.NA (Numerical Analysis); math.NT (Number Theory); math.OA (Operator Algebras); math.PR (Probability); math.QA (Quantum Algebra); math.RT (Representation Theory).
Selected 29 of 292 available items for this weekly brief.