1033 matching entries · Page 15 of 21
For the nearest-neighbor cosine XY model on the square lattice, the free-box thermodynamic two-point correlation at critical inverse temperature obeys C(r)=B_XY r^(-1/4)(log r)^(1/8)(1+o(1)) along a coordinate axis, with 0<B_XY<∞.
There is a two-dimensional ramified regular local ring A of mixed characteristic (0,5) for which K₅(A)→K₅(Frac A) has a nonzero kernel.
Every finite symmetric tensor category over an algebraically closed field of positive characteristic has an exact faithful strong symmetric monoidal functor to some finite higher Verlinde category Ver_{p^n}(k).
For every algebraically closed field K of characteristic p>0 and every fixed bound on defect-group order, blocks of finite groups represent only finitely many K-linear Morita-equivalence classes.
For a smooth strictly convex planar billiard with positive boundary curvature, a continuous foliation of a full near-grazing phase annulus by individually invariant essential curves forces an analytic boundary and a jointly analytic collar of smooth strictly convex caustics.
The truth of existential–universal sentences over the reals is decidable in one fixed level of the counting hierarchy, even when their integer polynomials are specified by arithmetic circuits; in particular, the existential theory of the reals lies in the counting hierarchy.
An explicit homogeneous hyperbolic polynomial of degree 20 in 23 real variables has a closed hyperbolicity cone that cannot be represented as the positive-semidefinite region of any finite real symmetric linear matrix pencil in the original variables.
For every eta in (0,1), there is a compact subset of [0,1] of measure greater than 1−eta that contains no affine copy of {2^(−n):n>=1} under any translation or nonzero real dilation of either sign.
For arbitrary complex F,G in L3(R²), the supremum of the triangular Hilbert transform over both finite hard-truncation endpoints is bounded in L^(3/2)(R²) by C times the two L3 norms.
For every eta > 0 and every sufficiently large integer N, there is a Littlewood polynomial with N consecutive coefficients in {−1,1} whose maximum modulus on the unit circle is at most (1+eta) sqrt(N).
Every nonempty connected bounded semialgebraic subset that is open in a complex affine algebraic variety is smooth and biholomorphic to a bounded symmetric domain if a discrete group of biholomorphisms acts properly with compact quotient.
For function fields of transcendence degree at least two over algebraically closed fields of characteristic different from a fixed prime ell, two perfect-closure field isomorphisms preserving the constant fields that induce the same pro-ell abelian-by-central Galois data up to ell-adic unit scaling agree up to Frobenius.
For every n≥2 and real K, each regular point of a noncollapsed RCD(K,n) space has an ambient-open neighborhood bi-Lipschitz to an open subset of Euclidean n-space, with distortion bounded only by n.
Every connected closed smooth Riemannian manifold of positive dimension whose global injectivity radius equals its diameter is, up to scale and isometry, a standard compact rank-one symmetric space.
For some sufficiently large even N, the cotangent bundle of S⁹×Sᴺ⁻¹ contains a closed exact smoothly embedded Lagrangian diffeomorphic to the base that is not Hamiltonian isotopic to the zero section.
For every closed connected smooth Riemannian manifold of dimension at least three with strictly negative sectional curvature, normalized Liouville measure has maximal entropy for the geodesic flow if and only if the metric is locally symmetric.
A finite connected three-dimensional CW complex satisfies the D(2) homological finiteness conditions but is not homotopy equivalent to any finite complex of dimension at most two.
For every finite group G and prime p with trivial largest normal p-subgroup, the poset of nontrivial elementary abelian p-subgroups of G has nonzero augmented reduced rational homology.
For any nontrivial smooth knot in the three-sphere, Dehn surgeries along distinct slopes never produce orientation-preservingly homeomorphic filled three-manifolds.
There are total Boolean functions whose bounded-error randomized query complexity cannot obey any universal bound of the form O((1+Q(f))^α) with α<4, where Q is bounded-error quantum query complexity.
For every finite N≥2, the undeformed SU(N) BFSS matrix quantum-mechanics Hamiltonian after removal of center-of-mass coordinates has exactly one normalizable zero-energy state.
For finite-range bounded interactions of fixed local dimension on any finite induced subgraph of the square lattice, a unique ground state separated by a uniform global spectral gap has entanglement entropy at most C times the crossing-edge boundary size for every set of sites.
A finitely generated group has two essentially free probability-measure-preserving actions with different costs: its Bernoulli action has cost strictly greater than one, while a suitable finite-height extension has cost closer to one.
Every finitely generated one-relator group containing no subgroup isomorphic to a Baumslag–Solitar group BS(m,n), with m and n nonzero, is word-hyperbolic.
For a symmetric n×n matrix whose entries on and above the diagonal are independent uniform signs, the probability of singularity is (1/2+o(1))^n.
For G=Spin(2n), n≥2, if three dominant integral weights sum to the root lattice, then a nonzero invariant in their tensor product after any positive integral dilation implies a nonzero invariant at the original weights.
For every finite group, every prime p, and every p-block B, the number of irreducible Brauer characters in B equals the number of conjugacy classes of B-weights.
A countable characteristic-zero division ring is algebraic over its center, generated by two elements as an algebra over that center, and infinite-dimensional over the center.
Over every characteristic-zero field, for a homogeneous ideal containing a regular sequence of any positive length with degrees at least two, a corresponding lex-plus-powers ideal has the same Hilbert function and at least as large a graded Betti number in every homological and internal degree.
For every fixed d≥3 and every sufficiently large even n, a deterministic algorithm outputs in polynomial bit time a simple connected nonbipartite d-regular n-vertex graph whose nonconstant adjacency eigenvalues lie strictly between ±2√(d−1).
The two-color graph Ramsey number of the n-dimensional binary cube is at most C·2^n for one absolute constant C.
For every fixed dimension d≥3, a constant c_d>0 makes every n-point set of distinct points in ℝᵈ determine at least c_d n^(2/d) distinct distances.
For every finite coloring of the positive integers and every k≥1, some k-element set has all its nonempty subset sums and all its nonempty subset products in one color class.
For every invertible mixing probability-preserving transformation and every fixed finite tuple of bounded measurable functions, consecutive multiple ergodic averages converge almost everywhere, along all positive averaging lengths, to the product of the functions’ integrals.
There are fixed positive rational ε and δ and a deterministic reduction mapping an End-of-Line instance of binary length N to a generalized circuit of length N(log N)^O(1). A solution to the original instance can be recovered in polynomial time from any polynomial-length rational assignment ε-satisfying all but a δ fraction of gates.
In each dimension, every convex body has isotropic constant no greater than that of a simplex, with equality only for simplices.
For every connected simple complex algebraic group G, smooth projective connected complex curve X, and complex level c outside Q, the full twisted D-module categories on Bun_G(X) and Bun_G-dual(X) are equivalent at dual shifted levels c and -1/(r c), retaining the given global forms and all connected components.
For every smooth connected projective complex variety whose anticanonical line bundle has a smooth Hermitian metric with semipositive curvature, some positive anticanonical tensor power has a nonzero global section.
If a smooth projective complex base satisfies all ordinary descendant Virasoro constraints, then the projectivization of every algebraic vector bundle of rank at least two over it satisfies them in every genus and individual integral curve class, with all cohomology insertions.
The ordinary discrete fundamental group of every connected smooth special compact Kähler manifold has an abelian subgroup of finite index.
Every smooth complex quintic threefold admits a numerical Bridgeland stability condition with the support property whose hyperplane-tensor and structure-sheaf spherical-twist symmetry shifts phase by 2/5, with the normalized central charge of Toda’s quintic Gepner conjecture.
At genus 10^60 with 3 times binomial(10^60,3) markings, an explicitly defined formal tautological class maps to zero in the Chow ring and rational cohomology of the compactified pointed-curve moduli space but lies outside the span of Pixton’s original graph-formula relations.
Every complex K3 surface has the convex approximation property: for every positive integer m, every holomorphic map from a neighborhood of a compact convex subset of C^m into the surface can be uniformly approximated there by entire maps C^m into it.
On a smooth connected compact Kähler manifold, if B is an effective rational simple-normal-crossing divisor with coefficients below one, M is a nef rational line bundle, K_X+B is pseudo-effective, and K_X+B+M is nef, then its real Bott–Chern first Chern class is represented by a semiample rational line bundle.
Assuming logarithmic Iitaka subadditivity for the specified smooth projective reduced-boundary fibrations, every analytically nef Q-Cartier log canonical divisor K_X+Delta on a normal irreducible compact Kähler space with effective rational boundary is semiample.
For a smooth proper hyperbolic curve over an algebraic closure of a p-adic local field and finitely many disjoint sufficiently small open disks, there is one connected finite étale cover with a component mapping isomorphically onto the entire disk exterior and every component above each disk having degree divisible by p.
Assuming the stated finite-level Ramanujan–Arthur decomposition, every occurring cuspidal excursion parameter for a split connected semisimple group over a global function field at a specified full finite level has one algebraic SL2 and commuting Weil centralizer map recovering the parameter on the entire Weil group, including inertia.
Every continuous odd absolutely irreducible two-dimensional 2-adic representation of the absolute Galois group of Q that ramifies at only finitely many finite primes occurs in the full completed varying-weight Hecke algebra at some odd tame level, possibly with auxiliary primes.
For arbitrarily large odd nonlinear powers, some Sobolev index k>8 admits a nonempty open set of Hᵏ initial data on the twelve-dimensional torus whose defocusing nonlinear Schrödinger solutions undergo classical finite-time self-similar blowup.
A complete smooth nonnegatively Ricci-curved metric on Euclidean space in dimension 16 has more harmonic functions of pointwise polynomial growth at most integer degree 50000 than Euclidean space has harmonic polynomials of that degree.
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arXiv · algebra-geometry — last successful metadata check: 21/10/2026, 07:20:46 UTC
arXiv · algorithms-formal — last successful metadata check: 21/10/2026, 07:19:48 UTC
arXiv · analysis — last successful metadata check: 21/10/2026, 07:21:51 UTC
arXiv · combinatorics — last successful metadata check: 21/10/2026, 07:18:49 UTC
arXiv · geometry-topology — last successful metadata check: 21/10/2026, 07:22:23 UTC
arXiv · logic-foundations — last successful metadata check: 21/10/2026, 07:23:04 UTC
arXiv · optimization-information — last successful metadata check: 21/10/2026, 07:23:10 UTC
arXiv · probability-dynamics-physics — last successful metadata check: 21/10/2026, 07:22:36 UTC
arXiv · theoretical-physics — last successful metadata check: 21/10/2026, 07:22:50 UTC
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