数学｜格物 GEWU

关于

K

等价代数簇的量子上同调环的猜想5 个问题

Monodromy of the crepant resolution identification versus derived autoequivalences for type A surface singularities
未解决约 19 年
Forbes–Jinzenji conjecture: $QH^*(\mathbb{P}(\mathcal{O}\oplus\mathcal{O}(k)\oplus\mathcal{O}(-2-k)))\cong QH^*(\mathbb{P}(\mathcal{O}\oplus\mathcal{O}(-1)\oplus\mathcal{O}(-1)))$ for all integers $k$
未解决约 20 年
Quantum flips after Lee–Lin–Wang: globalizing the quantum-cohomology embedding under simple flips, and the accompanying singularity, uniqueness, linearity, and Cayley-combinatorics questions
未解决约 6 年
Ruan–Wang K-equivalence conjecture for Gromov–Witten theory: all-genus invariance for ordinary flops, decomposition of K-equivalent maps, and global convergence of the quantum potential
未解决约 25 年
Directed double-point degeneration: an algebraic-cobordism route to quantum-ring invariance under ordinary flops (Question 8.3.1 of Lee–Lin–Qu–Wang)
未解决约 12 年

关于半群上一类重要同余的一个系列推广模式5 个问题

关于不同模覆盖系的厄尔多斯（Erdős）问题8 个问题

关于倒数和发散序列的厄尔多斯-图兰（Erdős-Turán）猜想6 个问题

关于码交换等价于前缀码的猜测8 个问题

关于奇数阶阿贝尔（Abel）群的Snevily猜想4 个问题

关于全纯双截曲率的猜想6 个问题

关于有限码具有有限完备化的判定问题9 个问题

关于有限域上代数曲线点数的Drinfeld-Vladt界5 个问题

关于闸轨道多重性的塞弗特（Seifert）猜想5 个问题

关于正则半群的两个嵌入问题5 个问题

光滑复完全交的沙利文（Sullivan）猜想6 个问题

广义度量空间问题4 个问题

广义倾斜模中的两个猜想8 个问题

广义斯梅尔（Smale）猜想4 个问题

哈茨霍恩（Hartshorne）猜想10 个问题

哈密顿（Hamilton）系统平衡点附近的不变环面7 个问题

亨特（Hunt）假设与Getoor猜测8 个问题

霍普夫（Hopf）猜想3 个问题

霍普夫（Hopf）问题4 个问题

基于有理多项式平方和的全局最优验证5 个问题

极小塔问题7 个问题

紧闭包与局部化相交换的问题8 个问题

紧流形上的闭测地线猜想7 个问题

经典拉姆齐（Ramsey）函数的估值1 个问题

The optimal constant for Ramsey goodness of cycles versus general graphs
未解决约 8 年

局部上同调模的相伴素理想的有限性问题7 个问题

矩阵的拓扑相似问题5 个问题

卡普兰斯基（Kaplansky）第六猜想5 个问题

凯莱（Cayley）图和相关的问题7 个问题

考克斯特群的胞腔7 个问题

柯克曼三元系大集的存在性问题10 个问题

拉丁方的横截问题8 个问题

拉姆拉斯（Ramras）问题6 个问题

朗兰兹（Langlands）纲领9 个问题

类数1实二次域的高斯猜想8 个问题

离散对数求解问题6 个问题

Monodromy of the crepant resolution identification versus derived autoequivalences for type A surface singularities

Quantum flips after Lee–Lin–Wang: globalizing the quantum-cohomology embedding under simple flips, and the accompanying singularity, uniqueness, linearity, and Cayley-combinatorics questions

Ruan–Wang K-equivalence conjecture for Gromov–Witten theory: all-genus invariance for ordinary flops, decomposition of K-equivalent maps, and global convergence of the quantum potential

Directed double-point degeneration: an algebraic-cobordism route to quantum-ring invariance under ordinary flops (Question 8.3.1 of Lee–Lin–Qu–Wang)

Open problems on quasi-absorbing elements in semigroups: order generation by quasi-primitive elements, semigroup-level duality, and Rees-congruence reduction

The congruence lattice of NI(X) for the exceptional finite sets ∣X∣=3|X|=3∣X∣=3 and ∣X∣=5|X|=5∣X∣=5

Congruences, embeddings, and automorphisms of the generalized bicyclic semigroups BωFB_\omega^{\mathscr{F}}BωF​ for arbitrary ω\omegaω-closed families F\mathscr{F}F

An intrinsic characterization of Condition (K) for inverse semigroups and their tight C*-algebras

DSC semigroups: which groups are DSC, and is the DSC class closed under direct products?

Minimal least common multiple of a distinct covering system with given minimum modulus: the open values Lmin⁡(m)L_{\min}(m)Lmin​(m) for m≥8m\geq 8m≥8

The weight-function threshold in the Erdős covering problem: which multiplicative weights force a positive density of uncovered integers

Sharp values of the k-th smallest modulus bound B(k) for covering systems with distinct moduli, and Selfridge's problem on avoiding the modulus 2 in the squarefree case

Explicit effective bounds for covering systems of the polynomial ring Fq[x]\mathbb{F}_q[x]Fq​[x]: making the minimum-degree constants of Li–Wang–Wang–Yi quantitative

Nonexistence of distinct covering systems with all moduli in [n,12n][n,12n][n,12n] for n≥4n \geq 4n≥4 (the Dalton–Jones interval problem)

Minimum multiplicity of the repeated modulus 9 in covering systems with odd moduli: is t9≤2t_9\le 2t9​≤2, and is the residue arrangement {4,5,r}(mod9)\{4,5,r\}\pmod 9{4,5,r}(mod9) realizable?

A uniform constant-factor improvement on tp≤p−ct_p \le p-ctp​≤p−c for covering systems with one repeated odd prime modulus (Question 5.3 of Harrington–Sun–Wong)

Existence of infinite exact distinct saturated covering systems with minimum modulus at least 5

Graham's conjecture: sets of lattice points with divergent reciprocal-square sum must contain infinitely many axis-parallel squares

Erdős's conjecture on arithmetic progressions (Jensen's zero-solution-set formulation): does every set of natural numbers with divergent reciprocal sum contain arbitrarily long arithmetic progressions?

Erdős conjecture on arithmetic progressions: does every set of positive integers with divergent reciprocal sum contain arbitrarily long arithmetic progressions?

Finiteness and value of M4M_4M4​, the supremum of reciprocal sums of sets of integers with no 4-term arithmetic progression

Erdős's reciprocal-sum conjecture for arithmetic progressions: the open cases k≥4k \ge 4k≥4

Erdős's harmonic-set (divergent reciprocal sum) conjecture: must every set of natural numbers whose reciprocals sum to infinity contain arbitrarily long arithmetic progressions?

Cardinality control for prefix-free codes preserving weighted occurrence sums: Kraizberg's weak commutative-equivalence approximation

Bounded cardinality discrepancy between a finite code and a weight-equivalent prefix-free code

Complete bayonet codes and finite maximal codes: the strong triangle conjecture beyond Hajós numbers and the realization problem

Companion Hajós factorizations for finite maximal codes: extending De Felice's Ω(n)≤2 theorem, the existence of non-Hajós codes, and the Zhang–Shum pair correspondence

Strong triangle conjecture for finite maximal codes and the embeddability of Shor's counterexample

The Schützenberger factorization conjecture for finite maximal codes and the associated finite-completion decision problems

Commutative regularity of Kleene closures of bounded semi-linear languages: extending Carpi–D'Alessandro's Theorem 1 beyond codes and the two-distinct-letters condition

Deciding embeddability of finite codes into finite maximal codes, and the open instance of Shor's counterexample code

A purely combinatorial proof of Snevily's conjecture on transversals of Cayley addition tables of odd-order abelian groups

The Kézdy–Snevily conjecture: f(n,2)=nf(n,2)=nf(n,2)=n for even nnn and f(n,2)>nf(n,2)>nf(n,2)>n for odd nnn (covering radius of sets of permutations in the Hamming permutation space)

The all-orders classification of subsquares of group multiplication tables without transversals (Müyesser–Pokrovskiy Conjecture 7.1)

Power-saving error term for the count of additive triples of bijections of a finite abelian group (toroidal semiqueens / complete mappings)

Extending the sharp dimension-estimate rigidity for polynomial-growth holomorphic functions to nonnegative holomorphic sectional curvature

Positive orthogonal holomorphic bisectional curvature on compact complex manifolds: is the Hermitian Frankel property rigid beyond the conformally Kähler setting?

Yau's uniformization conjecture for complete simply connected Kähler manifolds with negatively pinched sectional curvature

Does nonnegative holomorphic bisectional curvature imply nonnegative isotropic curvature on Kähler manifolds of complex dimension at least three?

Holomorphic convexity and polynomial-growth holomorphic functions on complete Kähler manifolds with nonpositive bisectional curvature and Euclidean volume growth (Question 1.10 of Wu–Yang)

Converse of the pseudoindex inequality for m-positive bisectional curvature on compact Kähler manifolds

Finite completions of codes within structured families: θ-invariant codes and strong alt-induced codes

Decidability of the inclusion problem for finite codes: deciding whether a finite code can be embedded in a finite maximal code

Good arrangements of the a∗wa∗a^*wa^*a∗wa∗-components of finite maximal codes and Krasner factorizations of cyclic groups

The embedding problem for the class of strong alt-induced codes: maximal extensions preserving regularity and finiteness

Decidability of the inclusion problem for finite codes: embedding a finite code into a finite maximal code

Finite completions of theta-invariant codes: which finite theta-invariant codes embed into a finite complete theta-invariant code?

Realizability of complete bayonet codes as slices CM(ω)C_M(\omega)CM​(ω) of finite maximal codes

Does Shor's bayonet code have a finite completion? The triangle conjecture for finite maximal codes

Completing codes with bounded deciphering delay inside submonoids of the free monoid

Attainable spectra of Tsfasman–Vlăduţ invariants of towers of global fields: infinite supports, order-rrr optimality over non-square finite fields, and minimal spectra

Exact limit of the Bassa–Beelen–Nguyen Drinfeld modular tower over an elliptic-curve coordinate ring

Improving the lower bounds for the Ihara constants A(2)A(2)A(2) and A(3)A(3)A(3) (toward determining A(q)A(q)A(q) for nonsquare finite fields)

Explicit optimal Drinfeld-modular towers beyond the polynomial ring: the remaining degree-two principal ideals

Closed-form Serre-type arithmetic refinements of Weil–Oesterlé bounds of order n≥3n\ge 3n≥3

Multiplicity of orthogonal geodesic chords in ball-diffeomorphic Riemannian manifolds with boundary focal points

Seifert's conjecture on the multiplicity of brake orbits in potential wells

At least n brake orbits for classical-type Hamiltonians: the generalized Seifert conjecture for disk-shaped potential wells

Hypothesis-free multiplicity of orthogonal geodesic chords in strongly concave Riemannian disks, and generic multiplicity among smooth metrics

Dispensability of the special-geodesic exclusion assumption in the multiplicity theorem for orthogonal geodesic chords in strongly concave Riemannian disks

Boone–Higman embeddings for semigroups: the word problem and finitely presented congruence-free monoids, with Maltcev's regular and bisimple embedding questions

Fundamental bisimple embeddings for solid regular and locally inverse semigroups (the Uniform Bands problem)

Problem 6.1 of Dékány–Szendrei–Szittyai: classifying the varieties of completely simple semigroups for which every E-solid locally inverse extension embeds into a λ-semidirect product

Explicit semiband embedding for semigroups whose regular D-classes are aperiodic semigroups

The Boone–Higman programme for semigroups: embedding finitely presented semigroups into finitely presented congruence-free, bisimple, and regular monoids

Diffeomorphism classification of smooth weighted complete intersections beyond the odd pairwise-coprime regime

The Sullivan Conjecture for complex projective complete intersections of dimension at least five: diffeomorphism classification beyond the homeomorphism theorem of Fang and Wang

Inertia groups of non-spin 4-dimensional complete intersections (Crowley–Nagy Conjecture 1.15)

Classification of smooth complete intersections by total degree, Pontrjagin classes, and Euler characteristic in complex dimension at least 8

The Sullivan conjecture for complete intersections: diffeomorphism classification in complex dimension at least 5

The Sullivan Conjecture for complete intersections of complex dimension at least 8

Existence and uniqueness of φ-fixed circles and φ-fixed discs for self-mappings on 𝔘-metric spaces (Özgür–Taş open problem)

Are the shortest-Hamiltonian-path, smallest-enclosing-ball, and entrywise ℓp\ell_pℓp​ matrix-norm functionals ggg-metrics of order n≥3n\ge 3n≥3 (for ℓp\ell_pℓp​, n≥2n\ge 2n≥2)?

Existence and homeomorphic classification of (m,n)(m,n)(m,n)-equidistant metric continua (Popvassilev's Problem 5.2 and Conjecture 5.1)

The open problems of Gaba-Agyingi-Leko on Chatterjea-type fixed point theory in partial b-metric spaces: sharp coefficient regime, T-stability, the P property, partial ultra-metric metrization, and the theta-phi-Chatterjea program

Submodule-closure of higher Ext-images En(RR)E_n(R_R)En​(RR​) over noetherian rings: Auslander's question for n≥3n \ge 3n≥3

Finiteness of injective dimension for (quasi-)Gorenstein generalized tilting modules over Artin algebras (Huang's Conjecture 4.7)

Tensorly faithful Wakamatsu tilting modules: classifying rings that force tensorly faithfulness and conditions weaker than the generalized Auslander-Reiten conjecture implying the Wakamatsu tilting conjecture

Wakamatsu Tilting Conjecture and Huang's Conjecture 4.7: finiteness and symmetry of the injective dimensions of generalized tilting modules over Artin algebras

The Wakamatsu tilting conjecture: is every Wakamatsu tilting module of finite projective dimension a classical tilting module?

The congruence lattice of NI(X) for the exceptional finite sets $|X|=3$ and $|X|=5$

Congruences, embeddings, and automorphisms of the generalized bicyclic semigroups $B_\omega^{\mathscr{F}}$ for arbitrary $\omega$ -closed families $\mathscr{F}$

Minimal least common multiple of a distinct covering system with given minimum modulus: the open values $L_{\min}(m)$ for $m\geq 8$

Explicit effective bounds for covering systems of the polynomial ring $\mathbb{F}_q[x]$ : making the minimum-degree constants of Li–Wang–Wang–Yi quantitative

Nonexistence of distinct covering systems with all moduli in $[n,12n]$ for $n \geq 4$ (the Dalton–Jones interval problem)

Minimum multiplicity of the repeated modulus 9 in covering systems with odd moduli: is $t_9\le 2$ , and is the residue arrangement $\{4,5,r\}\pmod 9$ realizable?

A uniform constant-factor improvement on $t_p \le p-c$ for covering systems with one repeated odd prime modulus (Question 5.3 of Harrington–Sun–Wong)

Finiteness and value of $M_4$ , the supremum of reciprocal sums of sets of integers with no 4-term arithmetic progression

Erdős's reciprocal-sum conjecture for arithmetic progressions: the open cases $k \ge 4$

The Kézdy–Snevily conjecture: $f(n,2)=n$ for even $n$ and $f(n,2)>n$ for odd $n$ (covering radius of sets of permutations in the Hamming permutation space)

Good arrangements of the $a^wa^$ -components of finite maximal codes and Krasner factorizations of cyclic groups

Realizability of complete bayonet codes as slices $C_M(\omega)$ of finite maximal codes

Attainable spectra of Tsfasman–Vlăduţ invariants of towers of global fields: infinite supports, order- $r$ optimality over non-square finite fields, and minimal spectra

Improving the lower bounds for the Ihara constants $A(2)$ and $A(3)$ (toward determining $A(q)$ for nonsquare finite fields)

Closed-form Serre-type arithmetic refinements of Weil–Oesterlé bounds of order $n\ge 3$

Are the shortest-Hamiltonian-path, smallest-enclosing-ball, and entrywise $\ell_p$ matrix-norm functionals $g$ -metrics of order $n\ge 3$ (for $\ell_p$ , $n\ge 2$ )?

Existence and homeomorphic classification of $(m,n)$ -equidistant metric continua (Popvassilev's Problem 5.2 and Conjecture 5.1)

Submodule-closure of higher Ext-images $E_n(R_R)$ over noetherian rings: Auslander's question for $n \ge 3$

When does the $\omega$ -torsionfree class $T_\omega(R)$ equal the generalized Gorenstein class $G_\omega(R)$ for a Wakamatsu tilting bimodule?

Cohomology of $B\mathrm{Diff}$ for connected sums of lens spaces beyond the generic non-diffeomorphic case

Hartshorne's conjecture on the Chow groups of hypersurfaces: is $A^i(X)=\mathbb{Q}[h^i]$ for $i<n/2$ ?

Rational smoothability of algebraic cycle classes: is $H^{2c}(X,\mathbb{Q})_{\mathrm{alg}}$ generated by classes of smooth subvarieties?

Is the smooth rational quartic curve in $\mathbb{P}^3$ a set-theoretic complete intersection?

Rational-curve determination of the nef-cone slope of rank-two vector bundles on Fano manifolds (the $\tau=\tau_0$ question of Muñoz–Occhetta–Solá Conde)

Existence of a smooth quadratic non-complete-intersection 11-fold in $\mathbb{P}^{17}$ of Fano index 8: the remaining case of Watanabe's classification of quadratic varieties with $n=2c-1$

Symmetry-rank thresholds for the Hopf conjecture under positive intermediate Ricci curvature: existence of a bound $d(k)$ for $k\ge 3$

Torus-symmetry thresholds for the Hopf conjecture under positive $k$ -th intermediate Ricci curvature with $k\ge 3$

The $\mathbb{Z}_2$ and $\mathbb{Z}_p$ Periodicity Conjectures: extending Adams's Hopf invariant one theorem from singly generated to periodic cohomology

Descent of nonnegativity certificates to rational coefficients: finite generation of $Pos(K)$ as a preordering of $\mathbb{Q}[x]$ for specific compact intervals with algebraic boundary, and archimedeanity of rational quadratic modules

Archimedean descent for finitely generated quadratic modules from $\mathbb{R}[X_1,\dots,X_n]$ to $\mathbb{Q}[X_1,\dots,X_n]$

Pseudointersection and tower numbers of topological Ramsey spaces: the Dobrinen–Navarro Flores questions on $\mathfrak{p}_\mathcal{R}\le\mathfrak{p}$ , $\mathfrak{p}_\mathcal{R}=\mathfrak{t}_\mathcal{R}$ , and values outside $\{\omega_1,\mathfrak{p}\}$

Generalized tower numbers at uncountable cardinals: the exact consistency strength of $\mathfrak{t}_\kappa>\kappa^+$ and the $\pi$ -depth equality $\pi\mathfrak{t}(U)=\pi\mathfrak{p}(U)$

Is the auxiliary cardinal $\mathfrak{d}^*$ equal to $\mathfrak{d}$ ? Optimal tower-refinement of filter-bases after $\mathfrak{p}=\mathfrak{t}$

Does $\mathfrak{p}(\kappa)=\mathfrak{t}(\kappa)$ hold for every uncountable regular cardinal $\kappa$ ? (the higher analogue of Malliaris–Shelah's $\mathfrak{p}=\mathfrak{t}$ )

Equality of the finitistic and full tight-closure annihilators in $F$ -pure local rings

Principal localization of tight closure and the existence of its failure in characteristic $p>2$

The closed geodesics conjecture for compact rank-one symmetric spaces: does every Riemannian metric on $S^n$ ( $n\ge3$ ), $\mathbb{CP}^m$ , $\mathbb{HP}^m$ , or the Cayley plane carry infinitely many geometrically distinct closed geodesics?

Finitely presented almost cyclic groups (Kourovka Notebook Problem 8.8b) and the second closed geodesic on closed $K(\pi,1)$ -manifolds

Duan–Long–Wang conjecture on the dichotomy of the number of prime closed geodesics on compact simply-connected Finsler manifolds with rational cohomology $T_{d,n+1}(x)$