7462 papers
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.
This paper establishes that moduli spaces of Scholze's -adic shtukas, including all local Shimura varieties for any group , satisfy a -adic rigid analytic version of Borel's extension theorem, thereby implying their -adic Brody hyperbolicity.
This paper establishes asymptotic upper and lower bounds for the number of planted plane trees with nodes and labels from that strictly decrease along any path from the root to a leaf, while also demonstrating an application of these results to calculating the largest eigenvalue of a tree's adjacency matrix.
This paper extends the author's previous result on solvable Lie algebras by proving that the Arens-Michael envelope and other completion homomorphisms for algebras of analytic functionals on connected complex Lie groups are homological epimorphisms, even without the assumption of solvability and including the case of Banach PI-algebras.
This paper establishes a homotopical version of the snail lemma and applies it to sequentiable families of arrows to derive a long exact sequence in a general category, which generalizes the classical long homology sequence when the category is abelian.
This paper establishes new local well-posedness results for nonlinear Schrödinger equations on general products of spheres and tori by deriving multi-linear Strichartz estimates via joint spectral projector bounds and proving a sharp estimate for the linear equation on the two-torus.
This paper establishes a new, simple criterion for generating spectral gaps in periodic word models, which yields new examples of ergodic Schrödinger operators with Cantor spectra of zero Hausdorff dimension that can simultaneously exhibit arbitrarily small supremum norms and arbitrarily long vanishing potential runs.
This paper presents a new polynomial-time adaptive algorithm based on Csirmaz's skeleton method for constructing convex approximation sets in multi-objective mixed-integer linear programs, which outperforms the current state-of-the-art approach by Helfrich et al. (2024) on various benchmark problems.
This paper investigates first- and second-order large deviations for stochastic differential equations with non-Lipschitz homogeneous drifts, demonstrating that the small-noise limit converges to the set of extreme deterministic solutions and that the second-order exponential behavior is governed by the ground state of an associated Schrödinger operator.
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.