7483 papers
This paper establishes that small Seifert fibered spaces with complementary legs generally fail to symplectically bound rational homology balls, thereby completing the classification of symplectically fillable contact structures on spherical 3-manifolds and revealing a sharp contrast with the smooth category.
This paper introduces an axiomatization of anticyclotomic Euler systems for a broad class of Galois representations, demonstrating how to construct universal Kolyvagin systems under minimal assumptions to derive results on Selmer group structures and Iwasawa main conjectures.
This paper establishes that an Ore extension satisfies the rank condition if and only if its coefficient ring does, while proving analogous results for strong rank conditions under specific automorphism hypotheses, and provides a new proof of Susan Montgomery's theorem regarding the direct and stable finiteness of skew power series rings.
This paper establishes necessary and sufficient conditions for extending a continuous mapping defined on a dense subset of a topological space to a weakly-continuous mapping on the entire space, without assuming separation axioms or compactness.
This paper establishes a scaling-invariant variational framework for steadily translating Sadovskii vortices that unifies patch and smooth cases, thereby proving their Lyapunov stability and demonstrating that perturbed solutions maintain their axis-touching geometry while propagating at nearly the same speed.
This paper proposes a dimension-independent Deep Learning method based on Physics-Informed Neural Networks (PINNs) to compute arbitrary eigenvalues of elliptic and nonlinear eigenvalue problems without requiring the prior calculation of lower eigenvalues.
This paper establishes that suitable weak solutions to the Navier-Stokes equations in remain smooth and regular up to if they belong to specific scaling-invariant mixed-norm spaces, including the critical case .
This paper establishes the rigidity of distance-preserving maps between bounded symmetric domains by proving that such maps exist only when the co-domain's rank is at least that of the domain, and when ranks are equal and the domain is irreducible, the maps are necessarily holomorphic or antiholomorphic triple homomorphisms, all derived using large-scale geometric tools without assuming map smoothness.
This paper introduces the Positivity Problem for nearly linearly recurrent sequences, a generalization of linear recurrences, and presents a decision procedure for order-two cases supported by a novel transcendence result for infinite series.
This paper investigates the sensitivity of inner models , constructed by replacing first-order logic with an abstract logic in Gödel's definition of , to the -extension of , demonstrating that can be consistently strictly smaller than and that this strict inequality follows from the existence of in specific cases.
This paper introduces PETLS, an efficient and flexible C++ library with Python bindings that implements novel algorithms for computing persistent topological Laplacians across various complex types to facilitate multiscale geometric analysis in machine learning.
This paper establishes a jointly -contracting action of filtrations on the space of graded norms for a polarized variety over a non-Archimedean field, thereby constructing non-Archimedean geodesic rays and infinite-dimensional flats while proving the convergence of relative limit measures along these rays.
This paper analyzes a continuous variant of Chaitin's Omega function defined by a sum over prefix-free Kolmogorov complexity, establishing its differentiability properties at density random points, characterizing the randomness of its values, and detailing the topological and computational features of its range and Turing invariance.
This paper establishes three applications of the length generating function for hyperbinary partitions, , by linking it to q-analogues of rational numbers in the Calkin-Wilf tree, characterizing the lattice of order ideals of specific fence posets, and expressing the entries of matrix products used to compute these q-analogues.
This paper extends Knightly and Reno's 2018 findings on weight-dependent symmetry in one-level densities to the centered moments of $GL(2)$ -functions by generalizing the weighted trace formula to arbitrary integers, analyzing resulting cross terms, and employing a combinatorial technique to facilitate comparison with random matrix theory.
This paper establishes twisted homological stability for handlebody mapping class groups with respect to both genus and the number of marked boundary discs by utilizing the categorical framework of Randal-Williams and Wahl and introducing the concept of coefficient bisystems, thereby extending previous results and enabling applications to moduli spaces of 3-dimensional handlebodies with tangential structures.
This paper presents a strategy for interpreting nonlinear characteristic-type penalty terms as numerical boundary flux functions, derived from a symmetric boundary matrix formulation of entropy flux, to guarantee provable entropy and energy stability for high-order discontinuous Galerkin methods solving nonlinear hyperbolic initial boundary value problems with open boundaries.
This paper characterizes the natural embedding of the twisted triality hexagon in by analyzing subspace intersections and establishing conditions for a set of lines to form such a hexagon, extending previous results on the split Cayley hexagon.
This paper investigates the homological properties of invariant rings under permutation groups, establishing that key invariants like the -invariant and quasi-Gorenstein property are independent of the field characteristic (except for specific shift behaviors in characteristic two), proving the Shank–Wehlau conjecture for permutation subgroups, and characterizing the ring of differential operators on these invariants.
This paper constructs a sequence of complete moduli spaces isomorphic to weighted projective spaces that parameterize specific -dimensional Calabi-Yau varieties associated with the Sylvester sequence, thereby generalizing the moduli of elliptic curves and Brieskorn's family of K3 surfaces while extending the theory of elliptic surfaces to higher dimensions.