7493 papers
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.
This paper establishes a sharp quantitative stability version of the Brascamp-Lieb inequality with a stability constant independent of the convex function, alongside uniform stability results for moment measures, by leveraging recent sharp stability versions of the Prékopa-Leindler inequality.
This paper generalizes scalar-valued holomorphic -contact and -symplectic structures to line bundle-valued analogues on compact complex manifolds, demonstrating that unlike their scalar counterparts, these new structures can admit projective examples, and investigates the positivity properties of their canonical bundles using recent regularisation results for -psh functions.
This paper establishes that the finite Osgood criterion on the drift term is both necessary and sufficient for finite-time blowup in the multiplicative stochastic heat equation on the interval , and extends this result to demonstrate instantaneous explosion on the real line by comparing solutions with those on the bounded domain.
This paper proposes a kinetic mathematical model for popularity-adaptive social networks that couples opinion dynamics with network evolution, introducing control laws to strategically influence connectivity and opinion spreading in order to mitigate polarization and foster consensus.
This paper establishes that the stability of -adjoint log canonical singularities on foliated surfaces undergoes sharp thresholds at and , which are proven to be optimal through a complete classification of these singularities for in terms of negative definite exceptional configurations.
This paper utilizes a computationally optimized variant of the Maximum Entropy Method to derive and prove two infinite families of non-Shannon entropy inequalities for five random variables, thereby advancing the understanding of the structure of the five-variable entropic region.
This paper presents methods to compute the number of -rational points with a specific -invariant on arbitrary modular curves, applying these techniques to classify the possible counts of cyclic -isogenies and points on Cartan modular curves for elliptic curves over number fields, while also providing an algorithm to determine the number of rational CM points.
This paper establishes a Faber-Krahn inequality for trees with a fixed matching number, a result that generalizes and implies the Klobůrštěl theorem regarding trees with specified numbers of interior and boundary vertices.
This paper presents the Reeb spaces of explicit real analytic functions that are not finite graphs, extending previous studies on smooth functions by incorporating topological considerations of level sets and real algebraic constructions.
This paper formulates and verifies a relative analogue of the Clemens conjecture for -log Calabi-Yau threefolds by establishing a perfect deformation/obstruction duality that suppresses virtual complications, thereby reducing relative Gromov-Witten invariants to classical enumerative counts of rational curves with balanced normal bundles.