数学｜格物 GEWU

球面上的

g

-猜想6 个问题

Regularity, shellability, polytopality, and ballness of the canonical stacked triangulations arising from the generalized lower bound conjecture
未解决约 22 年
Nevo's conjecture for 4-spheres without large missing faces: is $g_2 \geq g_1$ ?
未解决约 17 年
Finding an explicit non-polytopal Bier sphere: the polytopality problem for Bier's deleted-join spheres
未解决约 2 年
The Nevo–Petersen conjecture: are the γ-vectors of flag homology spheres f-vectors of balanced simplicial complexes?
未解决约 17 年
Smoothability of moment-angle manifolds over sphere triangulations
未解决约 13 年
Nonnegativity of $\gamma_2$ for flag simplicial spheres: the first nontrivial case of Gal's conjecture
未解决约 21 年

曲面到四维欧氏空间的等距浸入的存在性8 个问题

曲面交线的高效可靠计算5 个问题

趋化性模型解的行为与模式形成问题4 个问题

群作用下全纯映射的刚性问题7 个问题

燃烧方程组间断解的数值计算方法7 个问题

如何解决反映变量粗测量下“维数祸根”问题3 个问题

弱Pinsker猜想5 个问题

萨克斯（Sacks）关于波斯特（Post）问题的度不变解问题和马丁（Martin）猜想9 个问题

三维流形分类问题9 个问题

三维椭圆和电磁场计算问题的

hp

自适应有限元方法8 个问题

三种狭义相对论和引力及其相互关系7 个问题

瑟斯顿（Thurston）有效纤维化猜想3 个问题

沙努尔（Schanuel）猜想9 个问题

设计既实用又安全的公钥密码系统5 个问题

声波和电磁波反散射问题的唯一性7 个问题

是否存在求解线性规划的强多项式时间算法？8 个问题

是否存在求解装箱问题的绝对近似算法2 个问题

是否存在一个稳定的一阶完全理论，它有大于一的有穷多个可数模型8 个问题

双黑洞系统的数值研究6 个问题

双曲猜想1 个问题

The Arithmetic Persistence Conjecture: does arithmetic hyperbolicity persist under extension of the base field?
未解决约 7 年

双曲型守恒律方程组差分方法对间断解的收敛性6 个问题

双圈覆盖猜想9 个问题

双线性希尔伯特（Hilbert）变换的

L^{p}

有界性5 个问题

水分子多尺度建模与计算6 个问题

斯梅尔（Smale）均值猜想8 个问题

随机排队网络的遍历性3 个问题

天体力学中的中心构型有限性猜想8 个问题

凸多边形与厄尔多斯-Szekeres（Erdős-Szekeres）问题6 个问题

凸多面体的

d

-步猜想6 个问题

图的重构猜想8 个问题

图的Pfaffian定向5 个问题

图灵（Turing）等价问题8 个问题

图灵（Turing）度的自同构问题6 个问题

推广的Lax猜想：双曲锥能表示为半定锥的一个截面5 个问题

椭圆曲线的BSD猜想8 个问题

Regularity, shellability, polytopality, and ballness of the canonical stacked triangulations arising from the generalized lower bound conjecture

Nevo's conjecture for 4-spheres without large missing faces: is g2≥g1g_2 \geq g_1g2​≥g1​?

Finding an explicit non-polytopal Bier sphere: the polytopality problem for Bier's deleted-join spheres

The Nevo–Petersen conjecture: are the γ-vectors of flag homology spheres f-vectors of balanced simplicial complexes?

Smoothability of moment-angle manifolds over sphere triangulations

Nonnegativity of γ2\gamma_2γ2​ for flag simplicial spheres: the first nontrivial case of Gal's conjecture

Existence of a smooth isometric immersion of the entire hyperbolic plane into R4\mathbb{R}^4R4

Existence of complete isometric immersions with flat normal bundle of hyperbolic space into space forms of larger curvature

Global smooth isometric immersions of two-dimensional Riemannian manifolds into R4\mathbb{R}^4R4

Flexibility of isometric immersions of two-dimensional metrics into R4\mathbb{R}^4R4: direct convex integration on the Poznyak curvature equation

Lowering Günther's bound: smooth isometric immersions of arbitrary Riemannian manifolds into semi-Euclidean spaces of dimension below c(n)

Local well-posedness of the flag geodesic equation: geodesics on the manifold of isometric immersions of a square into R3\mathbb{R}^3R3

Global C2C^2C2 isometric immersion of the hyperbolic plane H2\mathbb{H}^2H2 into R4\mathbb{R}^4R4

Isometric regular immersion of the entire Lobachevsky (hyperbolic) plane into Euclidean 4-space E4E^4E4

Validated ODE-based approximation of surface-to-surface intersection curves: extension to tangential intersections, higher-order segment continuity, and certified step control

Certified approximate parameterization of intersection curves of general implicit surfaces: topology guarantees, computable error constants, and a priori distance bounds

Correctness and validity scope of the rotation-index stopping rule for tracing closed surface-intersection loops

Certified tangential-area bounding and error estimation for BVH-based surface–surface intersection with osculating toroidal patches

Certified topology by values for surface–surface intersection curves: validated eigenvalue criteria and conditioning analysis for Lagrange-basis Bézoutian matrix pencils

Mechanism arresting runaway aggregation and selecting stable, uniformly spaced finite aggregates in the Keller–Segel model of starved C. elegans L1 larvae

Phenotypic heterogeneity and the chemotactic instability in Keller-Segel-type models: pattern-onset thresholds and the global-existence/blow-up dichotomy for phenotype-structured autoattraction populations

Does logistic growth prevent blow-up in the fully parabolic Keller–Segel chemotaxis system in dimensions N≥3N\ge 3N≥3?

Blow-up of supercritical-mass solutions for the two-dimensional fully parabolic Keller–Segel system on the plane (Calvez–Corrias open problem)

Dynamics of subgroups of Aut(X_1) x Aut(X_2) on spaces of holomorphic maps between Hermitian symmetric spaces

Characterizing holomorphic fiber spaces whose every holomorphic self-map preserves a fiber

Infinitesimal rigidity criteria for CR mappings beyond finite nondegeneracy, and the local structure of the mapping moduli space

Holomorphic rigidity of Teichmüller space without the codimension hypothesis

Rigidity of lattice-symmetric proper holomorphic maps between balls at arbitrary Hölder boundary regularity

Structure of proper holomorphic maps between reducible bounded symmetric domains: rank-1 factors, general reducible targets, and semi-product maps beyond rank conditions

Realizable Hermitian-invariant symmetry groups Γf\Gamma_fΓf​ of rational proper maps between balls: characterization and minimal realization cost

Rigorous asymptotic solution of the one-dimensional discrete-source detonation problem in the point-source, zero-delay limit

Low-Mach-number and carbuncle-free robustness of the all-shock reactive Riemann solver for thermally perfect gases

Subcell-resolution methods for advection–reaction equations with stiff sources: non-splitting high-order-in-time integration and implicit-solver compatibility on coarse meshes

Existence and admissibility of the discontinuous steady deflagration families in the kinetic-theory recombination model (regimes 1(c) and 2(c) of Conforto–Monaco–Ricciardello)

A priori prediction of the spurious weak-detonation regime in fractional-step shock-capturing computation of stiff detonations

Global-in-time existence and wave-interaction structure of the generalized Riemann problem for the scalar Chapman–Jouguet combustion model

Predictive stability theory and convection-compatible source-term evaluation for high-order fractional-step shock-capturing methods with stiff reaction terms

Adaptive data-driven choice of the regularization parameter for deconvolution estimation of P(X<Y) with unknown error distributions

Smooth backfitting for errors-in-variables additive models with estimated error distributions and super-smooth errors

Convergence rates and optimal bandwidth matrices for kernel deconvolution density estimation with multivariate panel data

Failure of the Weak Pinsker Property for actions of non-amenable sofic groups

The weak Pinsker property beyond amenability: the sofic group boundary and a homological characterization

Kalikow's uniform martingale questions: finite-alphabet and minimal-alphabet representations of measure-preserving transformations

Does there exist a non-Bernoulli K-automorphism all of whose nontrivial splittings consist of one Bernoulli and one non-Bernoulli factor?

Finitary factors of i.i.d. processes with no finitary i.i.d. factor (Gabor's Open Problem (i))

Steel's uniformization conjecture for Turing-invariant functions: the global form of Martin's conjecture

Natural many-one degrees and the optimal set-theoretic hypotheses for the uniform Martin conjecture on m-degrees

Martin's Conjecture: the classification of Turing-invariant functions under the axiom of determinacy (parts 1 and 2)

Bard's Question 5.1: does the locally generated family Jx\mathcal{J}_{\mathbf{x}}Jx​ exhaust all uniformly Turing-invariant functions on a single Turing degree?

Steel's uniformity conjecture: is every Turing-invariant function equal on a cone to a uniformly Turing-invariant function?

The Slaman–Steel question: is Turing equivalence hyper-recursively-finite?

Martin's Conjecture in the enumeration degrees: the Wadge order on the Scott domain, jump-skip iterates, non-uniform regressive functions, and cone theories under Turing Determinacy

The regressive case of Martin's conjecture on the arithmetic degrees

Open questions from Part 1 of Martin's Conjecture for order-preserving and measure-preserving functions: the Rudin–Keisler position of the Martin measure, the hyperarithmetic degrees, and ZF provability

Is the 3-manifold homeomorphism problem in NP?

Wall's conjecture: is every finitely presented 3-dimensional Poincaré duality group the fundamental group of a closed aspherical 3-manifold?

Is the homeomorphism problem for closed 3-manifolds in NP? NP recognition of the remaining Thurston geometries

Bounded-runtime homeomorphism problem for finite-volume hyperbolic manifolds

Recognizing surface presentations of 3-manifold groups: decidability beyond the two-generator case and Whitehead degree bounds (Null's Questions 4.18 and 4.19)

Decidability of equality of hyperbolic volumes of finite-volume hyperbolic 3-manifolds

Wall's conjecture for Poincaré duality groups of dimension 3

Elementary-recursive effectivity of 3-manifold classification: Kuperberg's Conjectures 9.1-9.3 and the complexity placement of the homeomorphism problem

Cannon's conjecture: word-hyperbolic groups with 2-sphere Gromov boundary are virtually cocompact Kleinian groups

Remaining obstacles to a fully optimal two-dimensional hp-AFEM: near-best conforming hp-partitions, degree-robust broken-to-conforming equivalence, p-robust a posteriori error control, and p-uniform solvers

Uniform elliptic regularity pickup for the Neumann–Poisson problem on vertex patches of shape-regular simplicial meshes (the Dong–Ern conjecture, Assumption 3.5)

Sharp scale-resolution conditions for wavenumber-explicit hp finite element analysis of the time-harmonic Maxwell impedance problem

Wavenumber-explicit hp-FEM quasi-optimality for high-frequency Maxwell equations: general geometries and practical transparent-boundary truncations

Convergence and rate-optimality of automatic hp-adaptive finite element methods for indefinite (frequency-domain) Maxwell equations

Polynomial-degree-robust a posteriori error estimation for hp-finite element discretizations of Maxwell's equations on general nonaffine element geometries

Open problems in hp-adaptive edge-element methods for time-harmonic Maxwell's equations: automatic anisotropic refinement for edge singularities, scalable variable-p solvers, and resonant regimes

Quasi-optimal hp estimates for projection-based interpolation on hexahedral elements

Open problems in the covariant 1/c21/c^21/c2 expansion of general relativity: radiative modes, matching to full GR, and quantization of non-relativistic gravity

The Type II non-relativistic geometric trinity of gravity: action-level teleparallel and symmetric-teleparallel Newton–Cartan theories from the 1/c expansion

Open problems in the torsional Newton–Cartan large-ccc expansion of general relativity: non-twistless torsion, torsion-coupled motion, inequivalent dynamics, and physical regimes

Simultaneously Galilean- and Carrollian-compatible affine connections: the general torsionful classification and the gravitational content they support

Conditions for recovering a potential-based Carrollian gravitational theory from general Carrollian metric-affine connections

Action principle for the equation-level Carrollian electric and magnetic limits of general relativity

Quantization and non-perturbative duals of non-relativistic and Carrollian Jackiw–Teitelboim gravity

An automorphic criterion for fibrations of arithmetic hyperbolic 3-manifolds (Dunfield–Ramakrishnan, Question 1.7)

Lackenby's strong Heegaard gradient conjecture: positive strong Heegaard gradient for closed hyperbolic 3-manifolds

Nevo's conjecture for 4-spheres without large missing faces: is $g_2 \geq g_1$ ?

Nonnegativity of $\gamma_2$ for flag simplicial spheres: the first nontrivial case of Gal's conjecture

Existence of a smooth isometric immersion of the entire hyperbolic plane into $\mathbb{R}^4$

Global smooth isometric immersions of two-dimensional Riemannian manifolds into $\mathbb{R}^4$

Flexibility of isometric immersions of two-dimensional metrics into $\mathbb{R}^4$ : direct convex integration on the Poznyak curvature equation

Local well-posedness of the flag geodesic equation: geodesics on the manifold of isometric immersions of a square into $\mathbb{R}^3$

Global $C^2$ isometric immersion of the hyperbolic plane $\mathbb{H}^2$ into $\mathbb{R}^4$

Isometric regular immersion of the entire Lobachevsky (hyperbolic) plane into Euclidean 4-space $E^4$

Does logistic growth prevent blow-up in the fully parabolic Keller–Segel chemotaxis system in dimensions $N\ge 3$ ?

Realizable Hermitian-invariant symmetry groups $\Gamma_f$ of rational proper maps between balls: characterization and minimal realization cost

Bard's Question 5.1: does the locally generated family $\mathcal{J}_{\mathbf{x}}$ exhaust all uniformly Turing-invariant functions on a single Turing degree?

Open problems in the covariant $1/c^2$ expansion of general relativity: radiative modes, matching to full GR, and quantization of non-relativistic gravity

Open problems in the torsional Newton–Cartan large- $c$ expansion of general relativity: non-twistless torsion, torsion-coupled motion, inequivalent dynamics, and physical regimes

Hyperbolic manifolds that fiber over $S^1$ in higher odd dimensions: existence, abundance, virtual fibration, and structure of the fibrations

Pellarin's operator-theoretic Schanuel conjecture for the Carlitz exponential over Tate algebras: regular $\mu$ -independence of $\exp_C$ -values

Unconditional generic solutions of equations involving the modular $j$ -function and its iterates

Is $G$ -disjointness of subfields of $\mathbb{C}$ a symmetric relation?

Unique determination of a perfectly conducting ball by finitely many electric far-field data: the size restriction $kR<\sqrt{2}$ and the minimality of four measurements

Combinatorics of the interior-point counterexample polytope $\mathrm{CEX}_n(t)$ : the $n$ -cube conjecture and the vertex–tropical-segment correspondence

Does Lascar rank at least $\omega^\omega$ force continuum many countable models? (Tanović's conjecture for superstable theories)

Vaught's conjecture for superstable theories of arbitrary $U$ -rank

Eventual non-isolation of generic types of simple superstable groups and the $\omega^\omega$ rank threshold for countable models

Convergence of Lax–Friedrichs and Godunov schemes for $2\times2$ nonstrictly hyperbolic systems with an isolated umbilic point beyond the symmetric $(a,b)=(3,0)$ prototype

Convergence of fully discrete Godunov and Lax–Friedrichs schemes for general $n\times n$ systems of hyperbolic conservation laws

Intrinsic $L^\infty$ bounds and convergence of entropy stable shock-capturing space–time discontinuous Galerkin schemes for multi-dimensional systems of conservation laws

Does a $\Sigma_5$ -flow imply an $H_5$ -flow? Unit-sphere flows versus oriented 5-cycle double covers

Small Oriented Cycle Double Cover Conjecture: does every simple 2-connected graph other than $K_4$ and $K_6$ admit an oriented cycle double cover with at most $n-1$ directed cycles?

$L^{p}$ boundedness of the bilinear Hilbert transform in the lower range $1/2<p\leq 2/3$