2089 papers
This paper demonstrates that while the direct sum of general representable -matroids is not necessarily representable, the direct sum of uniform -matroids is always representable over a sufficiently large field, a result established through algebraic and geometric tools involving cyclic flats.
This paper introduces the Alternating Subspace Method (ASM), a novel sparse recovery algorithm that integrates greedy and splitting strategies by enforcing data fidelity within a subspace, thereby guaranteeing global convergence and achieving fast local geometric convergence on LASSO problems while demonstrating high efficiency and flexibility across various applications.
This paper investigates the contact process on dynamical random trees with degree-dependent edge updates, establishing sufficient conditions for a positive critical infection rate on general graphs and characterizing phase transitions—specifically proving strong survival for any infection rate under certain offspring distributions and providing a complete phase transition analysis for power-law trees with product kernels.
This paper investigates how key properties of probability monads, including their Kleisli laws, monoidal structures, and affinity, arise from their codensity presentations, establishing new universal properties for these monads and characterizing their tensor products via Day convolution while highlighting the limitations of the Giry monad on standard Borel spaces.
This paper establishes that the normal Lebesgue trace satisfies the Gauss-Green identity and occupies an intermediate regularity class between distributional and strong traces, enabling the proof of uniqueness for weak solutions to continuity equations on bounded domains under relaxed boundary regularity assumptions, while demonstrating that such assumptions remain necessary when characteristics enter the domain.
The paper demonstrates that every Hardy field can be extended to an -free Hardy field, a result that connects to classical oscillation criteria and is used to resolve questions posed by Boshernitzan and generalize one of his theorems.
This paper generalizes the local-relative correspondence beyond maximal contacts by identifying genus zero relative Gromov–Witten invariants of a smooth projective variety with a smooth nef divisor against specific orbifold invariants of multi-root stacks over a -bundle, thereby enabling the computation of relative invariants via absolute invariants of toric bundles.
This paper establishes a complete time-harmonic scattering theory for hyperbolic space by introducing a hyperbolic Sommerfeld radiation condition and Rellich theorem to uniquely define far-field patterns, thereby solving direct scattering problems and initiating the study of inverse scattering for obstacles and media in this geometry.
This paper establishes a general framework for visible Lagrangians in Hitchin systems that factor through proper subvarieties of the Hitchin base, computes their fiber-wise Fourier-Mukai transforms to construct mirror dual branes, and provides a detailed new example arising from pillowcase covers that connects to Hausel's toy model.
Inspired by Pan's work, this paper provides a new proof that an overconvergent modular eigenform of weight $1+kp$, achieved by demonstrating that the theta operator coincides with the Fontaine operator.
This paper provides a complete description of the Poisson boundary for wreath products under conditions where lamp configurations stabilize and the projected measure on is Liouville, thereby resolving a long-standing open question regarding the boundary for () with finite first moment measures.
This paper constructs a large family of pairwise non-isomorphic hyperelliptic curves mapping birationally into abelian surfaces isogenous to products of elliptic curves to generate rational equivalences in the Chow group of zero-cycles, thereby providing progress toward Beilinson's conjecture on the vanishing of the kernel of the Albanese map.
This paper investigates the distribution of -smooth polynomials over finite fields with prescribed coefficients by employing character sum estimates, adapting Bourgain's argument, and analyzing double character sums.
This paper establishes an equivalence between crystals on the prismatic site and modules with integrable quasi-nilpotent -connections, demonstrating that their cohomology is computed by a -de Rham complex and providing a geometric construction of the prismatic Sen operator that yields an explicit description of the action of on de Rham cohomology.
This paper presents algorithms grounded in invariant theory to address geometric problems concerning curves and hypersurfaces, with a primary focus on those of genus 2, 3, and 4, while also incorporating new theoretical results derived from the first author's PhD thesis.
This paper investigates the distribution of zeros for a specific class of polynomials and their derivatives, ultimately proving a weak variant of Sendov's conjecture for polynomials whose zeros are real and share the same sign.
This paper introduces and analyzes the convergence of a proximal-type algorithm with line search and inertial methods for solving DC programs under the Kurdyka-Łojasiewicz property, demonstrating its effectiveness in variable selection for linear regression.
This paper characterizes the conditions under which the band-unfolding of a nested prismatoid results in a nonoverlapping layout, demonstrating that the previously known counterexample is essentially the only obstruction to this method's success.
This paper identifies three necessary conditions for the existence of acyclic T-odd orientations, defines and characterizes polynomial graph classes where these conditions are sufficient, and provides constructive polynomial-time algorithms to build such orientations for these classes and their Cartesian products.
This paper establishes the well-posedness of a cubic nonlinear Schrödinger equation with irregular coefficients in the regime by introducing and proving the existence, uniqueness, and classical compatibility of "very weak solutions," while also validating these findings through numerical experiments.