Clay weekly context brief for the Maths category (ISO week 2026-W32).

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. Entropy-stable positivity-preserving DG schemes for Boltzmann-Poisson models of collisional electronic transport along energy bands
   Source: math.NA (Numerical Analysis)
   Link: https://arxiv.org/abs/1911.00593
   This work is related to the development of entropy-stable positivity-preserving DG methods as a computational scheme for Boltzmann-Poisson systems modeling the probability density of collisional electronic transport along energy bands in semiconductors.
2. Multivariate counting of wild abelian extensions
   Source: math.NT (Number Theory)
   Link: https://arxiv.org/abs/2607.27364
   Let $K$ be a global function field of characteristic~$p$ and let $G$ be a finite abelian group of exponent $p^e$.
3. Small value probabilities of additive and derivative martingales in supercritical branching Brownian motions and super Brownian motions
   Source: math.PR (Probability)
   Link: https://arxiv.org/abs/2607.27612
   In this paper, we establish asymptotics for the small value probabilities of additive and derivative martingales in both supercritical branching Brownian motions and super Brownian motions, thereby extending the corresponding results for Galton--Watson processes and continuous-state branching processes.
4. On equivalence classes of dissipative Hamiltonian pencils
   Source: math.RA (Rings and Algebras)
   Link: https://arxiv.org/abs/2607.27218
   We study matrix pencils of the form $\lambda E - (J-R)Q$, where $Q^*E = E^*Q \geq 0$, $J^* = -J$, $R^* = R \geq 0$, and $\lambda E - Q$ is regular, in the framework of Pokrzywa's ordering of strict equivalence orbits.
5. From Kreweras walks to branching perimeter processes of percolated triangulations
   Source: math-ph (Mathematical Physics)
   Link: https://arxiv.org/abs/2607.28566
   In this note, using a result of Bernardi, Holden and Sun, we give an explicit geometric relation between the perimeter of the peeling process along the percolation interface of a triangulation, and the corresponding Kreweras walk.
6. $\alpha\beta$-Tessarine Toolbox: A high-performance MATLAB framework for hypercomplex tensor algebra
   Source: math.AC (Commutative Algebra)
   Link: https://arxiv.org/abs/2607.27809
   The \textit{$\alpha\beta$-Tessarine Toolbox} is introduced as a high-performance MATLAB framework for generalized hypercomplex tensor algebra.
7. Families of curves separating points
   Source: math.AG (Algebraic Geometry)
   Link: https://arxiv.org/abs/2607.27746
   We show that for a hyperbolic curve X over an algebraically closed field k of characteristic zero and a finite set S of k-rational points of X, after replacing X by a finite \'etale cover, there exists a family of curves over X whose fibres over points in S have pairwise nonisogenous Jacobians.
8. Remarks on some quasi-linear fourth order parabolic equations arising in mathematical physics
   Source: math.AP (Analysis of PDEs)
   Link: https://arxiv.org/abs/2607.27451
   This note proves existence and uniqueness of strong solutions to a broad class of fourth-order quasi-linear parabolic equations in the class of Wiener spaces.
9. Components in characteristic $p$ and Quillen's conjecture
   Source: math.AT (Algebraic Topology)
   Link: https://arxiv.org/abs/2607.27500
   The purpose of this paper is to show that, under mild inductive assumptions, if a group $G$ contains a component that is a simple group of Lie type in characteristic $p$ and $O_p(G) = 1$, then the Quillen poset of $G$ at $p$ has nonzero rational homology.
10. Curved Kakeya problems and the projective geometry of paths
   Source: math.CA (Classical Analysis and ODEs)
   Link: https://arxiv.org/abs/2607.27629
   We introduce a general framework for curved Kakeya problems in $\mathbb{R}^n$, encompassing those arising from H\"ormander-type oscillatory integrals.
11. Stronger Lower Bounds for Tree Covers via Cyclic Symmetry
   Source: math.CO (Combinatorics)
   Link: https://arxiv.org/abs/2607.27264
   A tree cover of an $n$-point metric space is a collection of $k$ dominating trees such that every pairwise distance is approximately preserved by at least one tree.
12. Gabi-Monads
   Source: math.CT (Category Theory)
   Link: https://arxiv.org/abs/2607.27846
   We study gabi-monads on skew-closed categories, extending the gabi-algebras of Berger, the second author, and Vercruysse beyond the linear case.
13. Coefficient estimates and Bohr phenomenon for pluriharmonic mappings in the polydisc
   Source: math.CV (Complex Variables)
   Link: https://arxiv.org/abs/2607.27272
   We introduce the class $\mathscr{P}_{\mathcal{H}_n^0}(\alpha)$ $(0\leq \alpha<1)$ of normalized pluriharmonic mappings in the setting of several complex variables.
14. Minimal hypersurfaces of Morse index one
   Source: math.DG (Differential Geometry)
   Link: https://arxiv.org/abs/2607.27444
   We prove that a complete, connected, embedded, minimal hypersurface in $\mathbb{R}^{n+1}$ with finite total curvature and Morse index one is the higher-dimensional catenoid.
15. Conditional Topomorphic Degree and Multivariate Mean Equicontinuity for Minimal Amenable Group Actions
   Source: math.DS (Dynamical Systems)
   Link: https://arxiv.org/abs/2607.27400
   Let $G$ be a countably infinite discrete amenable group acting minimally on a compact metric space $X$, and let $\pi:X\to X_{\mathrm{eq}}$ be the maximal equicontinuous factor map.
16. Projective norm-attainments and their implications
   Source: math.FA (Functional Analysis)
   Link: https://arxiv.org/abs/2607.28054
   We show that nuclear norm-attaining operators (resp.\ polynomials) are always $w^*$-dense in the space of integral operators (resp.\ polynomials).
17. Character Fourier Spectra of Circular Units and Twisted Bernoulli Class Components
   Source: math.GM (General Mathematics)
   Link: https://arxiv.org/abs/2607.27503
   Let $\chi$ be a primitive odd Dirichlet character of conductor $f$.
18. The Hartman--Mycielski construction in topological MV-algebras
   Source: math.GN (General Topology)
   Link: https://arxiv.org/abs/2606.08541
   Recently, topological MV-algebras have been investigated by several mathematicians.
19. Centralizer Excess as an Obstruction to Carlson's Depth Conjecture
   Source: math.GR (Group Theory)
   Link: https://arxiv.org/abs/2607.27672
   Let $G=\operatorname{SmallGroup}(128,859)$ and let $k=\overline{\mathbb{F}}_2$.
20. An $S^2 \times S^2$ embedding
   Source: math.GT (Geometric Topology)
   Link: https://arxiv.org/abs/2607.27619
   In this note, we give a positive answer to K3 problem 4.28b, giving the first examples of homology 3-spheres that embed smoothly in $S^2 \times S^2$ but not $S^4$.
21. Green Cell-Free Massive MIMO for ISAC: Joint Cloud, Fronthaul and Radio Resource Allocation
   Source: math.IT (Information Theory)
   Link: https://arxiv.org/abs/2607.27778
   Cell-free massive MIMO (CF-mMIMO) combined with integrated sensing and communication (ISAC) is a promising architecture for future 6G networks, enabling new sensing-based applications.
22. Real $K$-Theory for $C^*$-Algebras: Just the Facts
   Source: math.KT (K-Theory and Homology)
   Link: https://arxiv.org/abs/2407.05880
   This work is intended to present the basic properties of $KO$-theory for real $C^*$-algebras and to explain its relationship with complex $K$-theory and with $KR$- theory.
23. On the Definability of Strong Negation in Bilateral Logics
   Source: math.LO (Logic)
   Link: https://arxiv.org/abs/2607.27252
   Recent work in bilateral logic has concerned itself with whether and to what extent strong negation, which "toggles" between assertion and denial, is definable in bilateral systems that lack it.
24. A Rank-Count Theory for the Combinatorial Discretizable Distance Geometry Problem
   Source: math.MG (Metric Geometry)
   Link: https://arxiv.org/abs/2607.27213
   The Distance Geometry Problem (DGP) asks for a geometric realization of a weighted graph with \(n\) vertices in \(\mathbb{R}^K\) such that Euclidean distances between vertices match the given edge weights.
25. A Stiff Order Condition Theory for Runge-Kutta Methods Applied to Semilinear ODEs
   Source: math.NA (Numerical Analysis)
   Link: https://arxiv.org/abs/2505.15099
   Classical convergence theory of Runge-Kutta methods assumes that the time step is small relative to the Lipschitz constant of the ordinary differential equation (ODE).
26. On the greatest common divisor of $n, \lfloor \alpha_1n\rfloor, \lfloor \alpha_2n^2\rfloor, ..., \lfloor \alpha_kn^k\rfloor$
   Source: math.NT (Number Theory)
   Link: https://arxiv.org/abs/2607.27533
   We answer a question of Bergelson and Richter about the probability of the relation $\gcd(n,\lfloor\alpha_1n\rfloor,\lfloor\alpha_2n^2\rfloor,...,\lfloor\alpha_kn^k\rfloor)=1$ for $n\in\mathbb{N}$ when $\alpha_1,...,\alpha_k$ are fixed irrational numbers.
27. Gaussian free field in annulus: BPZ equations and crossing probabilities for level lines
   Source: math.PR (Probability)
   Link: https://arxiv.org/abs/2607.27786
   We consider level lines of Gaussian free field (GFF) in annulus with alternating boundary conditions.
28. Hidden decay in the inverses of acyclic matrices
   Source: math.RA (Rings and Algebras)
   Link: https://arxiv.org/abs/2607.27220
   It is well-known that the absolute values of the entries of the inverse of a diagonally dominant tridiagonal matrix decay away from the diagonal.
29. Integrability in Asymptotic Symmetries of Spacetime: the $\text{BMS}_3$ scenario
   Source: math-ph (Mathematical Physics)
   Link: https://arxiv.org/abs/2607.28454
   We revisit the proof of a $\mathfrak{bms}_3-$integrable hierarchy introduced in Fuentealba et al.

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.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.LO (Logic); math.MG (Metric Geometry); math.NA (Numerical Analysis); math.NT (Number Theory); math.PR (Probability); math.RA (Rings and Algebras).
Selected 29 of 316 available items for this weekly brief.