数学｜格物 GEWU

椭圆算子的谱渐近以及韦尔-贝里（Weyl-Berry）猜想3 个问题

Classification of generator-remainder behaviours for meromorphic continuation of the renewal transform in Koch-snowflake fractal sprays
未解决约 2 年
Converse spectral problem for fractal strings with regularly varying gauge functions
未解决约 29 年
Lattice-case eigenvalue counting asymptotics for Laplacians on generalized Sierpiński carpets
未解决约 16 年

微分代数簇的不可缩分解8 个问题

The generalized Ritt problem: uniform bounds on differentiations for detecting components of differential ideals, equivalently definability in families of irreducibility of differential varieties
未解决约 76 年
Definability of primality for radical differential ideals and the generalized Ritt problem (Harrison-Trainor–Klys–Moosa Conjecture 1.1)
未解决约 18 年
The generalized Ritt problem: computing the essential prime components of a radical differential ideal
未解决约 53 年
The Ritt problem: algorithmic containment of prime differential ideals and essential prime decomposition of radical differential ideals
未解决约 90 年
Completeness of projective differential algebraic varieties: classification, the zero-dimensional test reduction, and the constant Kolchin polynomial question
未解决约 12 年
Deciding strong irreducibility of ascending chains and computing prime decompositions of perfect ideals of differential-difference polynomials
未解决约 17 年
Small irreducible components of arc spaces in positive characteristic: component status, transfer of arc-sharpness, curve selection at arc-blunt points, and birational elimination
未解决约 7 年
The Jacobi bound conjecture for prime differential ideals presented by generators
未解决约 161 年

微分封闭域上的平凡强极小集8 个问题

韦斯（Weiss）有限局部本原图猜想10 个问题

维特（Witt）代数的自同构群问题5 个问题

位相型分布的最小表示6 个问题

魏因施泰因（Weinstein）猜想7 个问题

稳定等价猜想7 个问题

西摩（Seymour）的二阶邻域猜想4 个问题

希尔伯特（Hilbert）第 16 问题6 个问题

希尔伯特第九问题：高斯二次互反律如何推广9 个问题

希尔伯特第十二问题：构作数域的最大阿贝尔扩域9 个问题

线性退化的拟线性双曲型方程组不会导致激波形成？7 个问题

相依结构下复杂删失数据统计建模问题3 个问题

薛定谔（Schrödinger）方程中的孤立子猜想7 个问题

雅可比猜想6 个问题

亚纯函数的亏量问题3 个问题

亚纯函数与其导函数有公共的波雷尔（Borel）方向吗？4 个问题

岩泽（Iwasawa）理论的主猜想7 个问题

杨-巴克斯特（Yang-Baxter）方程8 个问题

样本量的增加能保持原估计的渐近性质吗？6 个问题

一类二阶完全非线性偏微分方程的格林（Green）函数3 个问题

一些代数的Gröbner-Shirshov基8 个问题

由导出范畴建立量子群和典范基9 个问题

游荡连续统存在性问题6 个问题

有理代数曲面的高效参数化与隐式化方法4 个问题

有理顶点算子代数的分类5 个问题

有限阿贝尔（Abel）群的Davenport常数8 个问题

有限个二次函数最大值的极小化问题7 个问题

有限维数猜想6 个问题

酉表示中的狄拉克（Dirac）算子6 个问题

宇宙监督假设8 个问题

长田（Nagata）猜想10 个问题

整数流猜想7 个问题

中山（Nakayama）猜想和广义中山（Nakayama）猜想9 个问题

朱莉娅（Julia）集的分形维数10 个问题

Classification of generator-remainder behaviours for meromorphic continuation of the renewal transform in Koch-snowflake fractal sprays

Converse spectral problem for fractal strings with regularly varying gauge functions

Lattice-case eigenvalue counting asymptotics for Laplacians on generalized Sierpiński carpets

The generalized Ritt problem: uniform bounds on differentiations for detecting components of differential ideals, equivalently definability in families of irreducibility of differential varieties

Definability of primality for radical differential ideals and the generalized Ritt problem (Harrison-Trainor–Klys–Moosa Conjecture 1.1)

The generalized Ritt problem: computing the essential prime components of a radical differential ideal

The Ritt problem: algorithmic containment of prime differential ideals and essential prime decomposition of radical differential ideals

Completeness of projective differential algebraic varieties: classification, the zero-dimensional test reduction, and the constant Kolchin polynomial question

Deciding strong irreducibility of ascending chains and computing prime decompositions of perfect ideals of differential-difference polynomials

Small irreducible components of arc spaces in positive characteristic: component status, transfer of arc-sharpness, curve selection at arc-blunt points, and birational elimination

The Jacobi bound conjecture for prime differential ideals presented by generators

Kodaira-Spencer rank distribution in Buium's delta-stratification of the moduli of principally polarized abelian varieties: simple abelian varieties, Jacobians, and Manin-kernel absolute dimensions

Geometrically trivial strongly minimal sets that fail ℵ0\aleph_0ℵ0​-categoricity: classification beyond arithmetic groups

Strong minimality and geometric triviality of generic differential equations (Conjectures 1.5 and 1.7 of DeVilbiss–Freitag)

Are geometrically trivial strongly minimal sets in differentially closed fields unimodular? (Nagloo's Conjecture 4.1)

Non-ℵ0\aleph_0ℵ0​-categorical geometrically trivial strongly minimal sets in DCF0DCF_0DCF0​ beyond arithmetic Fuchsian groups (Casale–Freitag–Nagloo, Question 2.15)

Statement (C2)(C_2)(C2​): binary algebraic independence of the solutions of a general planar algebraic vector field

Ax-Schanuel for the first Painlevé equation

Algebraic independence of Painlevé transcendents at non-generic parameter values

Existence of locally-3n:23^n{:}23n:2 graphs with nontrivial third iterated local kernel Gx[3]G_x^{[3]}Gx[3]​

The Weiss conjecture for locally primitive graphs with almost simple or product action local type

The Weiss conjecture: valency-only bounds on vertex stabilizers of locally primitive vertex-transitive graphs and its equivalent second-singular-value formulation

Is every semiprimitive transitive permutation group graph-restrictive? (the converse implication of the Potočnik–Spiga–Verret conjecture)

Uniform Kazhdan–Margulis neighbourhoods for cocompact lattices with dense projections in products of quasi just-non-compact tdlc groups (Caprace–Le Boudec, Question 5.1)

Tornier's finiteness conjecture for discrete groups acting on trees with semiprimitive local action and an involutive inversion

Graph-restrictiveness of semiprimitive groups with a regular normal nilpotent subgroup: the exceptional cases where 2 or 3 divides the degree (the Potočnik–Spiga–Verret conjecture)

Bounding vertex-stabilisers in finite vertex-transitive graphs: the Weiss, Praeger, and PSV conjectures

The Weiss conjecture for primitive local actions of almost simple, simple diagonal, and product action type

The Weiss conjecture: is the order of a vertex stabiliser in a finite locally primitive vertex-transitive graph bounded by the valency alone?

Determine the automorphism group of the rank-nnn Witt algebra Wn=Der C[x1,…,xn]W_n=\mathrm{Der}\,\mathbb{C}[x_1,\dots,x_n]Wn​=DerC[x1​,…,xn​] (equivalently the polynomial automorphism group Aut C[x1,…,xn]\mathrm{Aut}\,\mathbb{C}[x_1,\dots,x_n]AutC[x1​,…,xn​]) for n≥3n\ge 3n≥3

Rota--Baxter operators beyond the homogeneous block-diagonal class and Novikov--Poisson structures on the full transposed Poisson algebra W(a,−1)\mathcal{W}(a,-1)W(a,−1)

Central extensions, derivations, and automorphisms of multi-copy semi-direct sums of the Witt algebra with its intermediate series modules

Non-surjective local and 2-local automorphisms of simple generalized Witt algebras with non-finitely generated grading group

Automorphism groups of Lie algebras of polynomial vector fields in infinitely many variables (the Bezushchak–Kashuba conjectures)

Minimal-order phase-type representations beyond three distinct real poles: extending the invariant-polytope construction to more, repeated, and complex poles, with global guarantees

The minimal positive realization problem: characterizing the minimal dimension of positive state-space realizations

Canonical representation of general phase-type distributions of order four and higher

Minimal-Norm Phase-Type Representations and the Minimal Maier Parameter Beyond Order Two

Efficient identification of all equivalent representations of Coxian phase-type distributions: permutation feasibility and complexity

A computable upper bound on the triangular order of phase-type distributions with real poles

The Weinstein conjecture for closed contact manifolds of dimension at least five

The multiplicity and elliptic-orbit conjectures for arbitrary Reeb flows on the standard contact sphere

The Weinstein conjecture in exact cotangent bundles: closed characteristics on compact contact-type hypersurfaces

Characterizing the open contact manifolds that satisfy the Weinstein conjecture

Strong Weinstein conjecture in dimension three: homologically trivial weighted cycles of closed Reeb orbits (Abbas–Cieliebak–Hofer conjecture)

Invariant Reeb orbits of strict contactomorphisms: Mazzucchelli's generalized Weinstein conjecture

The Weinstein conjecture for closed contact manifolds of dimension at least five

Conjecture 5.18 (Zhang, 2025): every finite weakly simple-minded system over a self-injective algebra is a simple-minded system

Stable-equivalence classification, scalar problems, and the Auslander–Reiten conjecture for self-injective algebras of polynomial growth

Cardinality of simple-minded systems in stable module categories (Koenig–Liu Question 6.1): does every simple-minded system over an artin algebra have exactly as many objects as the non-projective simples?

Auslander–Reiten conjecture on stable equivalences: invariance of the number of non-projective simple modules

Completing the classification of Erdmann's algebras of dihedral, semi-dihedral and quaternion type up to stable equivalence of Morita type: the surviving scalar-parameter problems

The Auslander–Reiten conjecture for stable equivalences: preservation of non-projective simple modules and the gluing-of-idempotents characterization

Conditional closure of stable equivalences of Morita type under tensor products, and completeness of the syzygy-algebra invariant B(ΩCe;C)B(\Omega_{C^e};C)B(ΩCe​;C)

The unresolved density regimes for Seymour's second neighbourhood conjecture on G(n,p)G(n,p)G(n,p): the critical case p=1/2p=1/2p=1/2 and the p→1p\to 1p→1 regime

Characterizing the P⃗\vec{\mathcal{P}}P-forcing graphs and the Second Neighborhood Conjecture for oriented graphs missing them

Seymour's second neighborhood conjecture: pushing the universal constant beyond 0.715538 and the limit of the nested weighted-minimizer/CSP method

Seymour's and Sullivan's second-neighbourhood conjectures for oriented split graphs and multipartite tournaments

The sharp upper bound on the number of algebraic limit cycles of planar polynomial vector fields (the simple version of Hilbert's 16th problem for algebraic limit cycles)

Realizable real schemes of M-curves of degree 9 with deep nests (Hilbert's 16th problem, part I, at the frontier degree)

The second part of Hilbert's sixteenth problem: finiteness and value of the Hilbert number H(n)H(n)H(n) for planar polynomial vector fields

The monomial-count variant of Hilbert's 16th problem: bounds for the Hilbert monomial number HM(m)\mathcal{H}^M(m)HM(m) and the Newton-polygon bound on periodic annuli

Open problems completing the zero-dimensional infinitesimal and tangential 16th Hilbert problem: higher-order Melnikov functions, Bautin index, bifurcation diagrams, real zero counts, and chains

Refined Ragsdale conjecture for M-curves of even degree: extremal bounds on even and odd ovals

Explicit reciprocity laws for Hilbert symbols over higher-dimensional local fields at the prime 2

Realizing the full Hilbert symbol, including its wild part, as a boundary map of a K-theory localization sequence, and a localization-theoretic proof of Hilbert reciprocity for number fields

The second reciprocity law for Pablos Romo's 3-cocycle symbols on a curve over a discretely valued field

The residue-characteristic-2 case of Shafarevich-style explicit formulas for the Hilbert pairing on complete higher-dimensional fields

Extending K-theoretic flag-symbol reciprocity to arithmetic bases: realizing Hilbert reciprocity over Spec⁡Z\operatorname{Spec}\mathbb{Z}SpecZ

Explicit reciprocity laws for formal Drinfeld modules without the congruence hypothesis, and their extension to higher local fields

Obstruction-free regimes for qqqth-degree power-residue reciprocity laws from Brauer-group exact sequences

The two-dimensional Contou-Carrère symbol: adelic two-dimensional class field theory

Generalizing the supplement to Scholz's reciprocity law: an odd-prime analogue and higher-power reciprocity for the primes above 2 in Q(pq)\mathbb{Q}(\sqrt{pq})Q(pq​)

Algebraicity of higher elliptic units for number fields with exactly one complex place (the unproven half of Morain's optimal-settings conjecture)

Nondegeneracy of the half-system matrix NℓN_{\ell}Nℓ​ and the completion of Koo–Yoon's explicit construction of class fields over cyclotomic fields

Extended Hecke class-field inclusions and missing ring class field data in the measured-foliation approach to Hilbert's 12th problem

Stark's unit conjecture for the theta-null generators of class fields of primitive CM fields: integrality of the theta-null Stark units ϵ(R)\epsilon(R)ϵ(R)

Hilbert's twelfth problem for totally real fields: complex-analytic generation of the maximal abelian extension

Algebraicity, reciprocity law, and Kronecker limit formula for higher elliptic units over number fields with exactly one complex place

The Charollois–Darmon conjecture: Stark unit arguments as periods of Hilbert Eisenstein series for ATR fields (Conjecture 4.1, 2008)

Geometrically trivial strongly minimal sets that fail $\aleph_0$ -categoricity: classification beyond arithmetic groups

Non- $\aleph_0$ -categorical geometrically trivial strongly minimal sets in $DCF_0$ beyond arithmetic Fuchsian groups (Casale–Freitag–Nagloo, Question 2.15)

Statement $(C_2)$ : binary algebraic independence of the solutions of a general planar algebraic vector field

Existence of locally- $3^n{:}2$ graphs with nontrivial third iterated local kernel $G_x^{[3]}$

Determine the automorphism group of the rank- $n$ Witt algebra $W_n=\mathrm{Der}\,\mathbb{C}[x_1,\dots,x_n]$ (equivalently the polynomial automorphism group $\mathrm{Aut}\,\mathbb{C}[x_1,\dots,x_n]$ ) for $n\ge 3$

Rota--Baxter operators beyond the homogeneous block-diagonal class and Novikov--Poisson structures on the full transposed Poisson algebra $\mathcal{W}(a,-1)$

Conditional closure of stable equivalences of Morita type under tensor products, and completeness of the syzygy-algebra invariant $B(\Omega_{C^e};C)$

The unresolved density regimes for Seymour's second neighbourhood conjecture on $G(n,p)$ : the critical case $p=1/2$ and the $p\to 1$ regime

Characterizing the $\vec{\mathcal{P}}$ -forcing graphs and the Second Neighborhood Conjecture for oriented graphs missing them

The second part of Hilbert's sixteenth problem: finiteness and value of the Hilbert number $H(n)$ for planar polynomial vector fields

The monomial-count variant of Hilbert's 16th problem: bounds for the Hilbert monomial number $\mathcal{H}^M(m)$ and the Newton-polygon bound on periodic annuli

Extending K-theoretic flag-symbol reciprocity to arithmetic bases: realizing Hilbert reciprocity over $\operatorname{Spec}\mathbb{Z}$

Obstruction-free regimes for $q$ th-degree power-residue reciprocity laws from Brauer-group exact sequences

Generalizing the supplement to Scholz's reciprocity law: an odd-prime analogue and higher-power reciprocity for the primes above 2 in $\mathbb{Q}(\sqrt{pq})$

Nondegeneracy of the half-system matrix $N_{\ell}$ and the completion of Koo–Yoon's explicit construction of class fields over cyclotomic fields

Stark's unit conjecture for the theta-null generators of class fields of primitive CM fields: integrality of the theta-null Stark units $\epsilon(R)$

Asymptotic stability of well-separated multi-solitons for the 1D $L^2$ -supercritical NLS in the full range $k>2$

Soliton resolution conjecture for the cubic-quintic nonlinear Schrödinger equation on $\mathbb{R}^3$

Deciding the component dichotomy for the Jacobian-one varieties $V_n^k$ : automorphism versus counterexample components and the two-dimensional Jacobian conjecture

Convergence of the compositional inverse and the noncommutative Jacobian conjecture in Popescu's theory of free biholomorphic functions on $B(\mathcal{H})^n$

Common Borel directions of a function of finite positive order and its q-difference operator $D_qf$

The full Iwasawa Main Conjecture for the $\mathrm{GL}_2 \times \mathrm{GU}(1)$ $p$ -adic $L$ -function over totally real fields in the non-split case

Greenberg's $\mu = 0$ conjecture for elliptic curves over $\mathbb{Q}$ : vanishing of the Iwasawa $\mu$ -invariant of Selmer groups over the cyclotomic $\mathbb{Z}_p$ -extension

The Iwasawa main conjecture for CM fields: equality of the Fitting ideal of Selmer modules with Katz's analytic $p$ -adic $L$ -function

Existence of simple involutive non-degenerate set-theoretic solutions of the Yang–Baxter equation of every cardinality $m^2 n$