7451 papers
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.
This paper establishes the existence of Eisenstein congruences between parallel weight Hilbert eigenforms and Eisenstein series over arbitrary totally real fields, demonstrating that these congruences arise from special values of Hecke -functions and determining conditions under which they can be satisfied by newforms.
This paper establishes that the set of locally finite Borel graphs with finite Borel asymptotic dimension is -complete by providing a combinatorial characterization for graphs generated by a single Borel function, which is subsequently used to classify the complexities of digraph homomorphism problems within this class.
This paper introduces a category of graph limits defined by vertex and edge distributions with morphisms as random maps, and utilizes category theory to establish the compactness of the space of all such limits under a newly defined convergence notion.
This paper establishes that functions within a Gaussian shift-invariant space can be uniquely recovered, up to a unimodular constant and conjugation, from their phaseless Hermite samples on a discrete set, and provides an explicit reconstruction algorithm for functions with finite coefficient sequences.
This paper establishes the profinite rigidity of various cusped finite-volume hyperbolic 3-manifolds, including specific link and knot complements, by demonstrating that profinite isomorphisms preserve Dehn fillings and utilizing this property to detect exceptional surgeries and characterizing slopes.
This paper establishes the existence and, under specific conditions, the uniqueness of equilibrium states for geometric potentials within a class of piecewise weakly convex interval maps that feature indifferent fixed points and non-Markov partitions.
This paper develops a specialized theory of diversities on by characterizing Minkowski linear and sublinear classes and establishing that finite diversities embed into these structures precisely when they satisfy conditions of negative type or correspond to generalized circumradii.
This paper introduces a correlation number for pairs of strictly positive, locally Hölder continuous potentials with strong entropy gaps on countable state Markov shifts, applying it to cusped Hitchin representations to explore its relationship with the Manhattan curve and establish associated rigidity properties.
This paper provides a complete description of the functional graph of the function over the finite field by determining its cycle lengths, counting cycles, and classifying the attached tree structures in terms of arithmetic invariants of .
This paper broadens the application of the -decoupling theorem to establish Strichartz and space-time bilinear estimates, thereby proving the unconditional uniqueness of solutions to the Boltzmann equation for Maxwellian particles and soft potentials with angular cutoff in both and settings.
This paper systematically studies the hyperpolygonal arrangements , introduced in 2024, by demonstrating their ability to discriminate between local properties, their projective uniqueness and combinatorial formality, and their role as the counterexample to Orlik's conjecture for .
This paper presents two distinct formulas—one explicit and one of the wall-crossing type—for calculating the motives of nullcones associated with quiver representations.
This paper characterizes the essential spectra and resolvent sets of off-diagonal block linear relations in Hilbert spaces by establishing precise spectral relationships with the products $AB$ and $BA$, and extends these results to relations involving Moore–Penrose inverses of closed linear operators with closed ranges.