Clay weekly context brief for the Maths category (ISO week 2026-W36). 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. Robust Assortment Optimization from Observational Data Source: math.ST (Statistics Theory) Link: https://arxiv.org/abs/2602.10696 Assortment optimization is a fundamental challenge in modern retail and recommendation systems, where the goal is to select a subset of products that maximizes expected revenue under complex customer choice behaviors. 2. Fukaya Algebra over $\mathbb{Z}$ Source: math.SG (Symplectic Geometry) Link: https://arxiv.org/abs/2411.14657 Given a closed, connected, relatively-spin Lagrangian submanifold in a closed symplectic manifold, we associate to it a curved, gapped, filtered, $A_{n, K}$-algebra over the Novikov ring with integer coefficients, which we extend to an $A_\infty$-algebra. 3. Variations of GIT Quotients and Dimer Combinatorics for Toric Compound Du Val Singularities Source: math.RT (Representation Theory) Link: https://arxiv.org/abs/2309.16112 A dimer model is a bipartite graph described on the real two-torus, from which we can define the associated quiver. 4. Morita Transport, Marked Projective Loci, and Dedekind Classification for C4-Type Conditionss Source: math.RA (Rings and Algebras) Link: https://arxiv.org/abs/2604.16326 Objectwise Morita invariance of $\Cfour$ is known. 5. Odd Khovanov homology and higher representation theory Source: math.QA (Quantum Algebra) Link: https://arxiv.org/abs/2311.14394 We introduce a super analogue of $\mathfrak{gl}_2$-foams, and use it to define an invariant of oriented tangles, shown to coincide with odd Khovanov homology when restricted to links. 6. Local law and delocalization for the Sachdev-Ye-Kitaev model Source: math.PR (Probability) Link: https://arxiv.org/abs/2608.03771 We establish a mesoscopic local law and quantitative eigenvector-delocalization estimates for the Sachdev--Ye--Kitaev model (SYK) Hamiltonian of $N$ interacting Majorana fermions. 7. Robust Chance-Constrained Optimization using a Continuous Parameter Space Wasserstein-2 Ambiguity Set of Gaussian Mixtures Source: math.OC (Optimization and Control) Link: https://arxiv.org/abs/2607.17018 We study distributionally robust linear chance-constrained problems in which uncertainty is modeled by a Gaussian mixture model (GMM). 8. Extensions of the Furstenberg-S\'ark\"ozy theorem via the arithmetic level-$d$ inequality Source: math.NT (Number Theory) Link: https://arxiv.org/abs/2605.16216 Green and Sawhney recently obtained a quasipolynomial bound in the Furstenberg--S\'ark\"ozy theorem for square differences by proving an ``arithmetic level-d'' inequality, thereby yielding a greatly improved density increment scheme. 9. An Extended 2+1-Dimensional Gardner Equation: On Moving Boundary Problems Solvable via Ermakov-Painlev\'e II Symmetry Reduction Source: math-ph (Mathematical Physics) Link: https://arxiv.org/abs/2608.28559 A class of moving boundary problems of Stefan-type for an extension of the 2+1- dimensional Gardner equation is shown to be amenable to exact solution by application of a Ermakov- Painlev\'e II symmetry reduction. 10. On the Egyptian knotted rope Source: math.HO (History and Overview) Link: https://arxiv.org/abs/2608.28072 The Egyptian knotted rope has been historically considered a measuring/geometric tool. 11. Spectral selections, commutativity preservation and Coxeter-Lipschitz maps Source: math.GR (Group Theory) Link: https://arxiv.org/abs/2505.19393 For a Coxeter system $(W,S)$ a self-map $\tau$ of $W$ such that $\tau_{\sigma\theta}\in \{\tau_{\theta},\ \sigma\tau_{\theta}\}$ for all $\theta\in W$ and all reflections $\sigma$ (analogous to being 1-Lipschitz with respect to the Bruhat order on $W$) is either constant or a right translation. 12. Equivariant Cohomology of Lie superalgebras Source: math.GM (General Mathematics) Link: https://arxiv.org/abs/2301.01270 In this article, we give Maurer-Cartan characterizations of equivariant Lie superalgebra structures. 13. First order equation on random measures as superposition of weak solutions to the McKean-Vlasov equation Source: math.FA (Functional Analysis) Link: https://arxiv.org/abs/2510.07542 The goal of this paper is to define an evolution equation for a curve of random probability measures $(M_t)_{t\in[0,T]}\subset \mathcal{P}(\mathcal{P}(\mathbb{R}^d))$ associated to a non-local drift $b:[0,T]\times\mathbb{R}^d \times \mathcal{P}(\mathbb{R}^d) \to \mathbb{R}^d$ and a non-local diffusion term $a:[0,T]\times \mathbb{R}^d \times \mathcal{P}(\mathbb{R}^d) \to \operatorname{Sym}_+(\mathbb{R}^{d\times d})$. 14. Statistical properties for irregular observables in slowly mixing hyperbolic systems Source: math.DS (Dynamical Systems) Link: https://arxiv.org/abs/2608.15569 We prove various statistical properties (i.e., decay of correlations, central limit theorems with convergence rates, maximal large deviations and almost sure invariance principles) for non-smooth observables in the form of indicators functions in polynomially mixing hyperbolic dynamical systems. 15. Phase Retrieval in $\mathbb C^4$ Requires Exactly Eleven Measurements Source: math.DG (Differential Geometry) Link: https://arxiv.org/abs/2607.27719 Determining the minimal number of intensity measurements required for phase retrieval in $\mathbb{C}^4$ has been a long-standing open problem. 16. K\"ahler thresholds Source: math.CV (Complex Variables) Link: https://arxiv.org/abs/2606.08224 The topology of K\"ahler manifolds is largely determined by the geometry due to its rigidity. 17. Applications of Borel-definable homological algebra to locally compact groups Source: math.CT (Category Theory) Link: https://arxiv.org/abs/2509.25474 We apply the description of the left heart of the category $\mathbf{LCPAb}$ of locally compact Polish abelian groups in terms of groups with a Polish cover and Borel-definable group homomorphisms to study injective and projective objects in the left heart of $\mathbf{LCPAb}$, as well as in the left hearts of its thick subcategories. 18. Discrepancy of geometric incidences Source: math.CO (Combinatorics) Link: https://arxiv.org/abs/2608.28354 We study the combinatorial (red-blue) discrepancy of finite point sets with respect to hyperplanes and, more generally, bounded-complexity affine algebraic sets. 19. New discretised polynomial expander and incidence estimates Source: math.CA (Classical Analysis and ODEs) Link: https://arxiv.org/abs/2601.01264 We present two applications of recent developments in incidence geometry. 20. Bounds for inertialess dynamo Source: math.AP (Analysis of PDEs) Link: https://arxiv.org/abs/2608.28584 We derive necessary conditions for instantaneous dynamo action for rotating convection. 21. Positive Geometry of Yang-Mills Correlators Source: math.AG (Algebraic Geometry) Link: https://arxiv.org/abs/2608.27594 We develop a positive-geometric formulation of tree-level Yang-Mills correlators in de Sitter space at three and four points through their helicity-stripped representatives on the cosmological Grassmannian. 22. Irrational components of the Hilbert scheme of points Source: math.AC (Commutative Algebra) Link: https://arxiv.org/abs/2405.11997 We construct irrational irreducible components of the Hilbert scheme of points of affine n-dimensional space, for n at least 12. 23. Coherent information deletion: Bayes' theorem and generalized Bayesian unlearning Source: math.ST (Statistics Theory) Link: https://arxiv.org/abs/2602.09061 Bayes' theorem admits an information-processing interpretation due to Zellner (1988): under the Shannon-information criterion, the posterior is the unique rule that processes prior and data information without information loss. 24. Tensor product degenerate spin affine Hecke superalgebras Source: math.RT (Representation Theory) Link: https://arxiv.org/abs/2607.28228 We define a new class of superalgebras, called tensor product degenerate spin affine Hecke superalgebras, and study their structure theory. 25. Singular ideals over arbitrary fields for the cyclic-headed snakes Source: math.RA (Rings and Algebras) Link: https://arxiv.org/abs/2506.19254 We study the Steinberg algebras with coefficients in an arbitrary field K for the cyclic-headed snake groupoids, which are basic examples of non-Hausdorff groupoids. 26. Law of the Iterated Logarithm for Weighted Sums of Functionals of Long-Memory Gaussian Sequences Source: math.PR (Probability) Link: https://arxiv.org/abs/2606.21006 We establish laws of the iterated logarithm for weighted sums of linear and nonlinear functionals of long-memory stationary Gaussian sequences. 27. Robust sensor coverage in the presence of spatial obstacles and exclusion zones Source: math.OC (Optimization and Control) Link: https://arxiv.org/abs/2607.11449 In this article, we develop a robust optimization framework for obstacle-aware aerial directional sensor networks operating under positional uncertainty using a sector-based sensing model. 28. Markov fractions and Cohn matrices Source: math.NT (Number Theory) Link: https://arxiv.org/abs/2604.17401 We show that the Markov fractions introduced recently by Springborn coincide with the index of the Cohn matrices defined by Aigner. Sources in this brief: math-ph (Mathematical Physics); math.AC (Commutative Algebra); math.AG (Algebraic Geometry); math.AP (Analysis of PDEs); 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.GR (Group Theory); math.HO (History and Overview); math.NT (Number Theory); math.OC (Optimization and Control); math.PR (Probability); math.QA (Quantum Algebra); math.RA (Rings and Algebras); math.RT (Representation Theory); math.SG (Symplectic Geometry); math.ST (Statistics Theory). Selected 28 of 257 available items for this weekly brief.