Clay weekly context brief for the Maths category (ISO week 2026-W42).

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. Invariant sets and spectral rigidity of Hamiltonian diffeomorphisms
   Source: math.SG (Symplectic Geometry)
   Link: https://arxiv.org/abs/2610.12279
   We solve a well-known question of Polterovich from 2002 regarding the rigidity of Hamiltonian diffeomorphisms in Hofer's metric in dimension two: every non-trivial Hamiltonian diffeomorphism of a surface of genus at least one has all positive iterations separated from the identity in Hofer's metric.
2. On the kernels of Lefschetz operators
   Source: math.AG (Algebraic Geometry)
   Link: https://arxiv.org/abs/2610.12091
   We study the kernels of Lefschetz operators arising from complete intersections of nef classes.
3. Equivariant noncommutative crepant resolutions and $G$-maximal modifying modules
   Source: math.AC (Commutative Algebra)
   Link: https://arxiv.org/abs/2610.11708
   Let $S$ be a Cohen-Macaulay normal domain containing a field $k$ with an action of a finite group $G$ with $|G|$ invertible in $k$.
4. Star-critical Ramsey numbers involving large generalized books
   Source: math.CO (Combinatorics)
   Link: https://arxiv.org/abs/2610.11151
   For graphs $F$, $G$, and $H$, we write $F \to (G, H)$ if every red/blue edge-coloring of $F$ contains either a red copy of $G$ or a blue copy of $H$.
5. Frobenius functors and $n$-torsionfree objects
   Source: math.RA (Rings and Algebras)
   Link: https://arxiv.org/abs/2609.25539
   We study $n$-torsionfree objects in abelian categories with enough projectives.
6. Quasi-quantum groups arising from cotensor coquasi-Hopf algebras
   Source: math.QA (Quantum Algebra)
   Link: https://arxiv.org/abs/2610.08361
   In this paper, we show that for any coquasi-Hopf algebra $H$ and any $H$-Majid bimodule $M$, the cotensor coalgebra $\operatorname{CoT}_H(M)$ admits a graded coquasi-Hopf algebra structure.
7. Brownian motion with drift conditioned to have restricted $L^2$-norm
   Source: math.PR (Probability)
   Link: https://arxiv.org/abs/2610.12354
   We study the long-time behaviour of Brownian motion with drift under a rare-event conditioning of the quadratic additive functional $Z_T=\int_0^T W_s^2ds$, where $(W_t)_{t\geq 0}$ is a Brownian motion with drift $\mu$.
8. Computing Lower Bounds on the Non-negative Rank via SAT Solvers
   Source: math.OC (Optimization and Control)
   Link: https://arxiv.org/abs/2610.11950
   Finding the extension complexity (xc) of a polytope is equivalent to finding the non-negative rank of its slack matrix.
9. Invariant Measures on Smooth Algebraic Groups over Higher Local Fields
   Source: math.NT (Number Theory)
   Link: https://arxiv.org/abs/2610.11468
   We construct a positive, finitely additive, left-invariant measure on the congruence cylinder ring of a smooth $d$-dimensional algebraic group over an $n$-dimensional local field.
10. Volume Sampling and Spectral Equalization in Randomized Alternating Projections
   Source: math.NA (Numerical Analysis)
   Link: https://arxiv.org/abs/2610.12346
   We study a family of randomized alternating projection methods that alternate among subspaces spanned by subsets of \(n\) vectors from a prescribed set.
11. Einstein-Cartan and Palatini-Cartan Gravity from Graded Poisson Geometry
   Source: math-ph (Mathematical Physics)
   Link: https://arxiv.org/abs/2610.11844
   Using notions from graded Poisson geometry, we develop a framework that allows for concise formulations of field theories such as Einstein-Cartan and Palatini-Cartan gravity.
12. A Dimension-Free Bound on the Poincar\'e Constant of Isotropic Log-Concave Measures
   Source: math.MG (Metric Geometry)
   Link: https://arxiv.org/abs/2610.07728
   The Kannan--Lov\'asz--Simonovits (KLS) conjecture asserts that isotropic log-concave probability measures have Poincar\'e constants bounded by a universal constant, independently of dimension.
13. A general framework for crystallization in maximal hard-core models
   Source: math.IT (Information Theory)
   Link: https://arxiv.org/abs/2610.11042
   We study general maximal hard-core models on periodic lattice-type graphs.
14. New Theorems on the Pentagon and the Pentagram
   Source: math.HO (History and Overview)
   Link: https://arxiv.org/abs/1908.00974
   We prove two pencil theorems for circumcenters in Miquel's pentagon and pentagram configuration.
15. Classifying Prime Character Degree Graphs With Eight Vertices
   Source: math.GR (Group Theory)
   Link: https://arxiv.org/abs/2603.15851
   In this paper, an effort is made to classify which prime character degree graphs having eight vertices occur for some finite solvable group.
16. On the Complexity of Finding Fixed Points for Set-Valued Contractions
   Source: math.GN (General Topology)
   Link: https://arxiv.org/abs/2609.14101
   In this paper, we study the computational complexity of finding fixed points for set-valued contractions.
17. The upper semi-Fredholm radius, extensions of restrictions, and subprojectivity
   Source: math.GM (General Mathematics)
   Link: https://arxiv.org/abs/2610.03835
   For a bounded operator $T$ between Banach spaces, let $d_+(T)$ be its distance to the operators that are not upper semi-Fredholm, and let $\inn(T)$ be Schechter's quantity $\inf\|T|_M\|$ over infinite-dimensional subspaces $M$.
18. Hyperplane winning for bad in manifolds
   Source: math.DS (Dynamical Systems)
   Link: https://arxiv.org/abs/2610.12037
   We prove the hyperplane winning property of weighted badly approximable vectors inside nondegenerate analytic manifolds and affine subspaces satisfying almost optimal Diophantine conditions.
19. The Hawking and Penrose singularity theorems for low regularity Finsler spacetimes
   Source: math.DG (Differential Geometry)
   Link: https://arxiv.org/abs/2610.11911
   We prove the Hawking and Penrose singularity theorems for Lorentz--Finsler structures of mixed horizontal/vertical regularity $C^{(1,2)}$ in the $C^1$ weighted case and $C^{(1,3)}$ in the unweighted case.
20. Hypercyclic Bergman-Toeplitz operators with some harmonic symbols
   Source: math.CV (Complex Variables)
   Link: https://arxiv.org/abs/2609.32650
   Little is known about the dynamics of Toeplitz operators on the Bergman space, and even in the case of harmonic symbols, few results are available.
21. Naturality characterizes product measures and relative product measures
   Source: math.CT (Category Theory)
   Link: https://arxiv.org/abs/2609.15909
   We show that the formation of the product measure is the only natural way to assign to each tuple of probability measures on measurable spaces a probability measure on the product space.
22. Romanovski polynomials, Gegenbauer connections, and $\mathrm{su}(1,1)$ ladder structures
   Source: math.CA (Classical Analysis and ODEs)
   Link: https://arxiv.org/abs/2608.17221
   We study the monic Romanovski (pseudo-Jacobi) polynomials with degree dependent parameters $\beta_K=-K$ and $\alpha_K=c/(K+1)$.
23. Bordisms and unbounded $KK$-theory
   Source: math.AT (Algebraic Topology)
   Link: https://arxiv.org/abs/2603.26450
   This monograph studies $KK$-theory in its unbounded model.
24. Uniqueness in inverse elastic scattering from traction-free polygonal obstacles with a single incoming wave
   Source: math.AP (Analysis of PDEs)
   Link: https://arxiv.org/abs/2610.11535
   In this article, we establish uniqueness in the inverse problem of time-harmonic elastic scattering from a bounded, traction-free obstacle in two dimensions.
25. Instanton and pillowcase homology of the $(-2,3,q)$ pretzel knots
   Source: math.SG (Symplectic Geometry)
   Link: https://arxiv.org/abs/2607.26096
   Hedden, Herald and Kirk conjectured that every knot admits a decomposition along a Conway sphere for which the Lagrangian Floer homology of the two associated immersed curves in the pillowcase recovers Kronheimer and Mrowka's reduced singular instanton homology.
26. K-Moduli Wall Crossing and Automorphic Forms for the Moduli Space of Rational Elliptic Surfaces
   Source: math.AG (Algebraic Geometry)
   Link: https://arxiv.org/abs/2610.10777
   Using K-moduli spaces for log quasimaps $q_t\colon\left(\mathbb P^1,\frac{1-t}{12}D\right)\to[\mathbb A^2/\mathbb G_m]$ of degree twelve with twelve points and weight $t/12$, we construct a modular interpolation $\{\mathcal M_t\}_{0\le t\le1}$ between the Baily--Borel compactification of the Heckman--Looijenga ball quotient $X_o$ and Miranda's GIT compactification of the moduli space of rational elliptic surfaces.
27. Derived functors and Hilbert polynomials over dominant Cohen-Macaulay rings
   Source: math.AC (Commutative Algebra)
   Link: https://arxiv.org/abs/2610.12120
   Let $(A,\mathfrak{m})$ be a Cohen-Macaulay local ring of dimension $d$, residue field $k$ and let $I$ be an $\mathfrak{m}$-primary ideal.
28. A counterexample to the Erd\H{o}s--S\'os bipartite-link conjecture
   Source: math.CO (Combinatorics)
   Link: https://arxiv.org/abs/2610.11642
   Erd\H{o}s and S\'os conjectured that every $n$-vertex $3$-uniform hypergraph whose link graphs are all bipartite has at most $(1/4+o(1))\binom n3$ edges.
29. The Classification of the Rota-Baxter Operators on Four-dimensional Grassmann Algebra
   Source: math.RA (Rings and Algebras)
   Link: https://arxiv.org/abs/2609.07377
   The purpose of this paper is to classify all the Rota-Baxter operators explicitly on Grassmann algebra in dimension four over the reals.
30. Shifted quantum affine superalgebras
   Source: math.QA (Quantum Algebra)
   Link: https://arxiv.org/abs/2610.05228
   For a quantum affine superalgebra with a fixed Drinfeld current presentation, we study shifted quantum affine superalgebras through a two-sided shifted Drinfeld current presentation, in which the leading degrees of the Cartan--Drinfeld currents are modified while the remaining current and Serre relations are retained.

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.GM (General Mathematics); math.GN (General Topology); math.GR (Group Theory); math.HO (History and Overview); math.IT (Information Theory); math.MG (Metric Geometry); math.NA (Numerical Analysis); math.NT (Number Theory); math.OC (Optimization and Control); math.PR (Probability); math.QA (Quantum Algebra); math.RA (Rings and Algebras); math.SG (Symplectic Geometry).
Selected 30 of 359 available items for this weekly brief.