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Cohen-Macaulayness of Local Models via Shellability of the Admissible Set

This paper proves that augmented admissible sets in Iwahori-Weyl groups are dual EL-shellable, thereby resolving a conjecture of Görtz and establishing the Cohen-Macaulayness of special fibers for local models with parahoric level structure—including previously open cases in residue characteristic 2 and non-reduced root systems—through a characteristic-free, intrinsic construction that yields an explicit shelling and inductive building procedure.

Xuhua He, Felix Schremmer, Qingchao Yu2026-03-09🔢 math

Gurau's spectral density is not a probability measure for individual real symmetric tensors

This paper demonstrates that while the "spectral density" derived from Gurau's resolvent trace yields valid probability measures on average for certain random tensor ensembles, it fails to correspond to a probability measure for individual deterministic tensors, thereby proving it is not a pointwise-defined probability distribution.

Maximilian Jerdee, Dmitriy Kunisky, Cristopher Moore2026-03-09🔢 math

Bayesian Linear Programming under Learned Uncertainty: Posterior Feasibility Guarantees, Scenario Certification, and Applications

This paper introduces a Bayesian framework for linear programming under learned uncertainty that integrates data-driven posterior updates with robust optimization and scenario-based strategies to provide rigorous, finite-sample feasibility guarantees and improved decision safety compared to naive approaches.

Debashis Chatterjee2026-03-09🔢 math

A Minimax Theory of Nonparametric Regression Under Covariate Shift

This paper establishes a minimax theory for nonparametric regression under covariate shift by introducing a transfer function to characterize convergence rates that range from classical benchmarks to accelerated regimes involving multiplicative sample size interactions, all achievable by a design-adaptive estimator even with unbounded covariate support.

Petr Zamolodtchikov2026-03-09🔢 math

Ground States of Attractive Fermi Schrödinger Systems with Ring-Shaped Potentials

This paper establishes the existence and nonexistence of ground states for mass-critical N-coupled attractive Fermi nonlinear Schrödinger systems in ring-shaped potentials based on the strength of interactions relative to a critical constant derived from a finite-rank Lieb-Thirring inequality, while also characterizing the mass concentration behavior of these states as the interaction strength approaches this critical threshold.

Yujin Guo, Yan Li, Shuang Wu2026-03-09🔢 math

Beamforming Optimization for Extremely Large-Scale RIS-Aided Near-Field Secure Communications

This paper proposes a joint optimization algorithm for transmit precoding and discrete phase-shift reflection in an extremely large-scale RIS-aided near-field secure communication system with artificial jamming, effectively maximizing secrecy rates even when eavesdroppers are located close to the RIS and in the same direction as legitimate users.

Xiaotong Xu, Qian Zhang, Yunxiao Li, Xuejun Cheng, Meihui Liu, Ju Liu2026-03-09🔢 math

Note on Morita equivalence in ring extensions

This paper establishes the Morita invariance of several classes of ring extensions and provides a counterexample of a class that is not Morita invariant, building upon previous results by Miyashita and Ikehata.

Satoshi Yamanaka2026-03-09🔢 math

On Weakly Separable Polynomials in Skew Polynomial Rings

This paper characterizes weakly separable polynomials in skew polynomial rings and explores the relationship between separability and weak separability in rings of derivation type, building upon the generalization of separable extensions introduced by Hamaguchi and Nakajima.

Satoshi Yamanaka2026-03-09🔢 math

PriorIDENT: Prior-Informed PDE Identification from Noisy Data

The paper proposes PriorIDENT, a prior-informed weak-form sparse-regression framework that integrates compact physics priors into dictionary construction to robustly identify governing partial differential equations from noisy spatiotemporal data while outperforming existing baselines in accuracy and stability.

Cheng Tang, Hao Liu, Dong Wang2026-03-09🔢 math

On weakly separable polynomials and weakly quasi-separable polynomials over rings

This paper generalizes and improves upon Hamaguchi and Nakajima's work by characterizing weakly separable polynomials over commutative rings using derivatives and discriminants, while also establishing necessary and sufficient conditions for such polynomials in noncommutative skew polynomial rings.

Satoshi Yamanaka2026-03-09🔢 math

Shape-Resonance in Spectral density, Scattering Cross-section, Time delay and Bound on Sojourn time

This paper revisits the Friedrichs model to derive precise asymptotic results, including the Breit-Wigner formula and spectral concentration, for resonances near embedded eigenvalues, while also establishing exact properties for sojourn time, scattering amplitude, and time delay in the context of rank-one perturbations of the Laplacian.

Hemant Bansal, Alok Maharana, Lingaraj Sahu, Kalyan B. Sinha2026-03-09🔢 math

Space-time boundaries for random walks and their application to operator algebras

This paper investigates the Martin boundary of space-time Markov chains associated with finitely supported random walks to establish structural connections between various compactifications and harmonic function boundaries, ultimately demonstrating that the noncommutative Shilov boundary of the associated tensor algebra coincides with its Toeplitz $C^*$ -algebra.

Adam Dor-On, Matthieu Dussaule, Ilya Gekhtman, Pavel Prudnikov2026-03-09🔢 math

A Note on Hodge theoretic anabelian geometry

Motivated by non-abelian Hodge theory, this paper formulates a Hodge-theoretic version of Grothendieck's anabelian conjecture by replacing Galois actions with natural $\mathbb{C}^\times$ -actions, proving an analog of Mochizuki's theorem for smooth projective hyperbolic curves over $\mathbb{C}$ and extending the result to higher-dimensional ball quotient manifolds.

Qixiang Wang2026-03-09🔢 math

Vanishing orders and zero degree Turán densities

This paper investigates the structural implications of vanishing $\ell$ -degree Turán densities in hypergraphs, proving that for $k$ -uniform hypergraphs with vanishing 2-degree Turán density, a specific global vertex ordering (2-vanishing order) must exist, thereby generalizing classical results on zero Turán density and demonstrating that unlike the classical case, 2-degree Turán densities accumulate at zero.

Laihao Ding, Hong Liu, Haotian Yang2026-03-09🔢 math

Sobolev mappings of Euclidean space and product structure

This paper establishes that Sobolev maps $f \in W^{1,2}$ on the product of two Euclidean domains with invertible differentials preserving or swapping the factor spaces are necessarily split when the dimension $n \ge 2$ , a result that fails for $n=1$ and for lower regularity spaces $W^{1,p}$ with $p<2$ .

Bruce Kleiner, Stefan Müller, László Székelyhidi Jr., Xiangdong Xie2026-03-09🔢 math

Metrical Distortion, Exterior Differential and Gauss's Lemma

This paper revises Gauss's Lemma by introducing the concept of "metrical distortion" as a non-identity isometry between double tangential and tangential spaces, and concretely defines the exterior differential via covariant gradient transport to incorporate a "differential slip" representing scalar gauge theory, ultimately distinguishing between geodesically radial volume preservation (metrical distortion) and length preservation (exponential mapping) through the example of the 2-sphere.

Stephan Voellinger2026-03-09🔢 math

The Planar Coleman--Gurtin model with Beltrami conductivity

This paper establishes the existence of regular global and exponential attractors with finite fractal dimension for the planar Coleman--Gurtin heat equation with memory and rough anisotropic diffusion encoded by a Beltrami coefficient, utilizing a combination of instantaneous smoothing techniques, maximal parabolic regularity, and quasiconformal estimates.

Francesco Di Plinio2026-03-09🔢 math

Local theta correspondence and Galois periods

This paper investigates the behavior of Galois periods under the local theta correspondence for even orthogonal and symplectic groups by comparing their multiplicities, constructing explicit transfer maps, and establishing both adjoint and relative character relations.

Chong Zhang2026-03-09🔢 math

Hausdorff dimension of images and graphs of some random complex series

This paper establishes the almost sure Hausdorff dimension of the images and graphs of a broad class of random complex series, which encompasses famous deterministic functions like the Weierstrass and Riemann functions, thereby providing a probabilistic framework to predict the exact dimension values of their deterministic counterparts.

Chun-Kit Lai, Ka-Sing Lau, Peng-Fei Zhang2026-03-09🔢 math

Numerical Algorithms for Partially Segregated Elliptic Systems

This paper introduces two numerical frameworks—a strong-competition penalty method with damped Gauss-Seidel iterations and a projected gradient method with an accelerated variant—to solve elliptic systems governed by nonconvex partial segregation constraints where three nonnegative components must have a vanishing pointwise product.

Farid Bozorgnia, Avetik Arakelyan, Vyacheslav Kungurtsev, Jan Valdman2026-03-09🔢 math

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