7471 papers
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.
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.