7444 papers
This paper investigates -transitivity and topological -recurrence for backward shift operators on weighted sequence spaces over directed trees, establishing specific equivalences between recurrence and hypercyclicity for both unrooted and rooted tree structures.
This paper investigates an unexpected abundance of doubly isogenous genus 2 curves with automorphism groups over finite fields, leading to the surprising construction of a global example over a number field, a theoretical limit on such instances via the Zilber–Pink conjecture, and potential applications in deterministic polynomial-time polynomial factorization.
This paper establishes that the operator norm of Fourier and dyadic paraproducts mapping between Hardy spaces and is comparable to the norm of the symbol function in the homogeneous Hardy space , where the exponents satisfy the relation .
This paper generalizes the concept of boundary pairs from locally compact groups to measured groupoids, demonstrating their structural properties in semidirect products and Poisson boundaries, and establishing the existence of equivariant maps to algebraic group quotients for ergodic groupoids with Zariski dense representations.
This paper establishes a functional version of the additive kinematic formula by combining the Hadwiger theorem on convex functions with a Kubota-type formula for mixed Monge-Ampère measures, thereby providing a new explanation for the equivalence of functional intrinsic volume representations and deriving a novel integral geometric formula for mixed area measures.
This paper classifies the conditions under which the edge ideal powers of a connected graph admit a minimal Lyubeznik resolution and characterizes when they are bridge-friendly, thereby guaranteeing a minimal Barile-Macchia cellular resolution.
This paper constructs unbalanced superalgebra structures on induced by a non-degenerate symmetric bilinear form and a base vector, then applies these findings to address problems in integer matrix factorization and the isometry of integral lattices.
This paper resolves a problem posed by Pavlović by constructing a harmonic K-quasiconformal analogue of the Koebe function, determining the optimal order for harmonic quasiconformal mappings with bounded Schwarzian norm to belong to Hardy spaces, and deriving associated pre-Schwarzian and Schwarzian norm estimates.
This paper proves the conjecture that multiscale differentials can be contracted level by level into Gorenstein singularities, demonstrating that the global residue condition governing their smoothability is a specific instance of the residue condition for descent differentials.
This paper utilizes Priestley and Esakia dualities to provide a comprehensive dual characterization of free algebras and coproducts in varieties of Gödel algebras, generalizing existing results to arbitrary numbers of generators and establishing that all free Gödel algebras are bi-Heyting.
This paper analyzes the structural relationships between shocks, instability, and competition interfaces in Brownian last-passage percolation, demonstrating how the divergence and alignment of shock trees for unstable eternal solutions can be used to reconstruct the instability region.
This paper establishes that very general L-equivalent K3 surfaces are D-equivalent by utilizing Hodge theory to relate distinct lattice structures via rational endomorphisms, while also partially extending these findings to hyperkähler fourfolds and moduli spaces of sheaves on K3 surfaces.
This paper establishes that under the generalized Heegner hypothesis and specific local conditions, the Pontryagin dual of the Bloch--Kato Selmer group for a modular form over an anticyclotomic -extension is free over the Iwasawa algebra, implying the vanishing of the associated Shafarevich--Tate groups and generalizing previous results on elliptic curves to both ordinary and non-ordinary settings.
This paper constructs a unified framework of topological -homology for rings with twisted -action, which generalizes existing theories like THH and THR, introduces new examples such as quaternionic THH, and establishes homotopical identifications with twisted free loop spaces via a novel family of crossed simplicial groups.
This paper proves unconditionally that a positive proportion of cubic Hecke -functions over the Eisenstein field do not vanish at the central point by establishing a new asymptotic formula for the mollified second moment, a result that overcomes the lack of a perfectly orthogonal large sieve bound in this unitary family through novel applications of Patterson's theta function, Heath-Brown's sieve, and a new Lindelöf-on-average bound.
This paper establishes that the space of framed infinite volume hyperbolic 3-manifolds is connected but not path connected by proving its connectivity via the density theorem for Kleinian groups and demonstrating the existence of non-tame manifolds whose framing sets form distinct path components.
This paper characterizes relevant cuts in graphs as minimum weight cuts between distinct vertices and proposes a method using Picard-Queyranne Directed Acyclic Graphs to accelerate their enumeration, validated through experimental comparison with state-of-the-art algorithms.
This paper establishes that for unbounded graph matroid families, the Whitney property (unique graph reconstruction from the matroid) is equivalent to the Lovász-Yemini property (maximal matroid rank), while also providing characterizations for the bounded case and demonstrating that these properties are preserved under unions and hold for all 1-extendable graph matroid families.
This paper explicitly determines the dual boundary complexes of normal crossings compactifications for the moduli spaces of maps with and , identifying them as moduli spaces of decorated metric graphs and proving their contractibility under specific conditions by analyzing the boundary strata of the Vakil--Zinger desingularization.
This paper establishes a strong comparison principle for elliptic solutions of the 3-D steady potential flow equation in spherical coordinates, overcoming the challenge of potential-dependent coefficients to address applications in supersonic gas dynamics.