P\'olya's conjecture for Neumann eigenvalues of spherical shells arXiv:2610.31464 Lenses make many points: Pure point spectrum disproves Simon's L^2 c... arXiv:2610.31637

Local Optimality of the d-cube for Laplacian Eigenvalues arXiv:2610.30463 Optimal Hardy weights for the fractional discrete Dirichlet Laplacia... arXiv:2610.31171 Lower bounds on Steklov eigenfunctions for a class of curvilinear po... arXiv:2610.31387

Harmonic-Einstein maps and critical metrics for eigenvalues of the c... arXiv:2610.28894 Property (R) with its stability for analytic functional system and u... arXiv:2610.29710 Rayleigh's conjecture for vibrating plates: simpler planar proof and... arXiv:2610.29840

P\'olya's conjecture for Dirichlet eigenvalues of spherical shells a... arXiv:2610.27707

Polynomial Spectral Gap Estimates for Finitely Differentiable Quasi-... arXiv:2610.26977 A periodic Anderson--Bernoulli model with infinitely many spectral gaps arXiv:2610.27160 The Spectrum of the Discrete Mathieu Operator with Nonreal Coupling arXiv:2610.27487

Spectra of Multivariate Vandermonde Matrices and Min-max Error Bound... arXiv:2610.24670 Efimov effect in an internal spectral gap of a three-particle lattic... arXiv:2610.26284

Signed dual graphs and face spectral gaps of Cayley 2-complexes arXiv:2610.22916

A note on the failure of Payne's inequality on manifolds with boundary arXiv:2610.20097

A note on the A.C. spectrum of limit-periodic Jacobi matrices arXiv:2610.19416 New Qualitative and Quantitative Estimates for Neumann Eigenvalues t... arXiv:2610.19455 Quantitative P\'olya inequalities for annular sectors arXiv:2610.19461

Resonance counting and spectral gaps for hyperbolic surfaces via Fou... arXiv:2610.17276 Optimization Inverse Spectral Problem for the Schr\"odinger Operator... arXiv:2610.18081 Square-Root Profiles and Sharp Fourier Decay of Quasiperiodic Spectr... arXiv:2610.18259

Semigroup properties of Schr\"{o}dinger operators with complex singu... arXiv:2610.16670 The Adiabatic b-Calculus and the Global Anomaly Formula on Manifolds... arXiv:2610.16938 (Sharp arithmetic) localization beyond transversality arXiv:2610.17139

Eigenspaces of Preserved Graph Laplacian Eigenvalues under Positive ... arXiv:2610.14310 A note on Guo's perturbation result for symmetric nonnegative matrices arXiv:2610.14759 An optimization problem for \delta' leaky stars arXiv:2610.15771

Non-Bloch band theory for finite banded non-Hermitian Toeplitz matrices arXiv:2610.13715 Sharp upper bounds for Steklov eigenvalues on warped products arXiv:2610.13738

On the inequality \mu_3 < \lambda_1 for the eigenvalues of the Lapla... arXiv:2610.13180 Sums of Dirichlet eigenvalues in proximity of the disk and the ball arXiv:2610.13256 Non-resonant angles in a Robin eigenvalue problem arXiv:2610.13601

Equivariant Steklov homogenisation and stability of spectral represe... arXiv:2610.12725 High-Index Asymptotics of Mathieu Spectral Gaps and Splittings arXiv:2610.12751 Quantitative spectral stability and sharp Fourier estimates for peri... arXiv:2610.12856

Dirac operators on periodic planar graphs: the right definition advo... arXiv:2610.10964 Elementary cellular automata: spectral properties of Koopman operato... arXiv:2610.10967

Smooth spectral statistics of random perturbations of Schr\"odinger ... arXiv:2610.09869 Maximisers for the second Neumann eigenvalue of annuli in two-dimens... arXiv:2610.10119

A long time Gutzwiller trace formula for perturbations of Schr\"odin... arXiv:2610.09046 Corner Regularity of Laplacian Eigenfunctions arXiv:2610.09095 Graph transformations and eigenvectors of the Laplacian, signless La... arXiv:2610.09599

Spectral gaps of double covers of hyperbolic surfaces arXiv:2610.07193 Kuznecov formulas for domains with fractal boundary arXiv:2610.08487 On the Dirac Faber-Krahn Conjecture arXiv:2610.08665

Block numerical ranges for linear relations arXiv:2610.04431 P\'olya's conjecture for Neumann eigenvalues of annuli arXiv:2610.05146 Planar Dirichlet eigenvalue bounds from a trace identity arXiv:2610.05636