2026-09-10

基于Viazovska八维方法，证明24维中Leech格是最密球堆积且为唯一最优周期堆积，构造了线性规划界的最优辅助函数。该研究给出素数域上Reed-Solomon码的确定性多项式时间列表译码算法，对任意评估集和常数速率逼近列表译码容量，解决该方向长期开放的核心问题。本文证明Aldous–Fill谱隙猜想：确定任意给定阶数连通简单正则图上简单随机游走的最…

The sphere packing problem in dimension 24 95

Tags: 球堆积 格论 线性规划界 几何
Source: arXiv Math.NT - Number Theory | 阅读原文

[摘要]
基于Viazovska八维方法，证明24维中Leech格是最密球堆积且为唯一最优周期堆积，构造了线性规划界的最优辅助函数。

Algorithmic List Decoding of Reed-Solomon Codes up to Capacity 95

Tags: 编码理论 列表译码 Reed-Solomon码 理论计算机
Source: arXiv CS.CC - Computational Complexity | 阅读原文

[摘要]
该研究给出素数域上Reed-Solomon码的确定性多项式时间列表译码算法，对任意评估集和常数速率逼近列表译码容量，解决该方向长期开放的核心问题。

The maximum relaxation time of a random walk on regular graphs 92

Tags: 随机游走 谱图论 组合数学 正则图
Source: arXiv Math.PR - Probability | 阅读原文

[摘要]
本文证明Aldous–Fill谱隙猜想：确定任意给定阶数连通简单正则图上简单随机游走的最大弛豫时间的渐近值，偶数阶极值为三次图、奇数阶为四次图，并给出定量稳定性。

Two global stability theorems for small-data $3 D$ compressible Euler solutions: Unique maximal globally hyperbolic developments with gradient-blowup & smooth global existence in the entire spacetime 88

Tags: 偏微分方程 激波 广义相对论 拟线性波动
Source: arXiv Math.AP - Analysis of PDEs | 阅读原文

[摘要]
证明三维可压缩欧拉方程小数据全局稳定性：一类数据形成激波，首次给出多维拟线性波动系统MGHD存在唯一性；另一类数据全局光滑存在，突破零条件限制，发现对数增强色散。

A sharp version of Talagrand's selector process conjecture, with applications to rounding fractional covers and Bernoulli Sudakov minoration 88

Tags: 概率论 组合数学 随机过程 猜想证明
Source: arXiv CS.DM - Discrete Mathematics | 阅读原文

[摘要]
证明Talagrand选择过程猜想的尖锐版本，统一强化其与Kahn-Kalai猜想，并应用于分数覆盖取整与Bernoulli测度Sudakov下界估计。

Exact Asymptotics for the 2D Euclidean Random Matching Problem 88

Tags: 概率论 随机匹配 渐近分析 偏微分方程
Source: arXiv Math.PR - Probability | 阅读原文

[摘要]
确定二维环面上随机二分匹配期望最优代价对任意幂次q≥1的一阶精确渐近，回答Talagrand问题，涉及p-Poisson方程能量与变分鞅问题、抛物型Monge-Ampère流。

Solution of uniform Tur\'an's Tetrahedron Problem 88

Tags: 极值组合 超图 图兰密度
Source: arXiv Math.CO - Combinatorics | 阅读原文

[摘要]
解决了图兰四面体问题的均匀版本，证明K4^(3)的均匀图兰密度为1/2，确认Rödl 1986年下界构造最优，是极值组合学的重要进展。

Monodromy Eigenvalues of Milnor Fibers for Line Arrangements 86

Tags: 超平面排列 代数几何 拓扑 单值
Source: arXiv Math.AG - Algebraic Geometry | 阅读原文

[摘要]
证明线排列Milnor纤维上同调单值特征值的组合消失准则，结合Hirzebruch不等式证得本质复线排列单值阶数至多5，复化实排列至多4，部分解决Papadima--Suciu猜想及连通性猜想。

Logarithmic $A_{m a t h r m {i n f}}$ -cohomology, Part II 86

Tags: p-adic几何 上同调 棱镜理论 数论
Source: arXiv Math.NT - Number Theory | 阅读原文

[摘要]
发展了对数A_inf上同调理论，建立与étale、de Rham及晶体上同调的比较同构，并给出半稳定局部系统C_st猜想的新证明。

Relative $$v a r p h i, G a m m a $$ -modules and $p$ -adic differential equations 86

Tags: p进几何 算术几何 (φ,Γ)-模 微分方程
Source: arXiv Math.NT - Number Theory | 阅读原文

[摘要]
建立仿射刚性解析空间上的不完全相对周期环，证明相对Fontaine-Cherbonnier-Colmez等价，并构造de Rham局部系对应的p进微分方程，推广Berger及Andreatta-Brinon工作。

A relative Langlands dual realization of $T^{\*} $G / K $$ and derived Satake 86

Tags: 几何表示论 Langlands对偶 导出范畴 对称空间
Source: arXiv Math.NT - Number Theory | 阅读原文

[摘要]
证明拟分裂对称空间余切丛与Langlands对偶群的圈对称空间对偶品种同构，将导出Satake等价推广至拟分裂对称空间，并联系扭仿射Grassmannian与几何Langlands。

Mirror Counts of Spectral Curves 85

Tags: 代数几何 辛几何 热带几何 镜像对称
Source: arXiv Math.AG - Algebraic Geometry | 阅读原文

[摘要]
研究凸格多边形对应的镜像计数问题，证明相对雅可比可构造层的镜像对偶，并用rulings等价计算节点有理曲线数，联系热带曲线与对数GW不变量。

Optimal Spectral Lower Bounds and Nonradial Nonlinear Asymptotic Stability of a Family of Three-Dimensional Keller--Segel Self-Similar Blow-Up Solutions 85

Tags: 偏微分方程 谱分析 非线性稳定性 Keller-Segel
Source: arXiv Math.AP - Analysis of PDEs | 阅读原文

[摘要]
该论文研究三维Keller-Segel系统自相似爆破解的谱性质与非径向非线性渐近稳定性，通过Sturm计数、波算子及Mellin-Newton二次型证明谱间隙最优下界为1/4，并建立稳定子空间上的指数衰减半群和调制稳定性。

Kobayashi Hyperbolicity of General Surfaces via the Poincar\'e Problem 85

Tags: 代数几何 双曲性 复几何 叶层理论
Source: arXiv Math.AG - Algebraic Geometry | 阅读原文

[摘要]
证明P^3中次数至少18的一般曲面不含有理或椭圆曲线，将Clemens的非常一般结果加强为Zariski开条件，并由此推出Kobayashi双曲性，解决Demailly-El Goul问题。方法基于2-jet微分诱导的多叶层及Poincaré型界。

Cohomological Hall algebras and Quot schemes of curves 85

Tags: 代数几何 表示论 Hall代数 Quot概型
Source: arXiv Math.AG - Algebraic Geometry | 阅读原文

[摘要]
研究曲线上的余调Hall代数及其对Quot概型同调的作用，引入虚拟同调，证明torsion CoHA同构于shuffle代数及Yang-Baxter算子对应的braided对称代数，确定尖点Quot概型的tautological关系并给出新基。

2026-09

2026-09-10

The sphere packing problem in dimension 24 95

Algorithmic List Decoding of Reed-Solomon Codes up to Capacity 95

The maximum relaxation time of a random walk on regular graphs 92

Two global stability theorems for small-data $3 D$ compressible Euler solutions: Unique maximal globally hyperbolic developments with gradient-blowup & smooth global existence in the entire spacetime 88

A sharp version of Talagrand's selector process conjecture, with applications to rounding fractional covers and Bernoulli Sudakov minoration 88

Exact Asymptotics for the 2D Euclidean Random Matching Problem 88

Solution of uniform Tur\'an's Tetrahedron Problem 88

Monodromy Eigenvalues of Milnor Fibers for Line Arrangements 86

Logarithmic $A_{m a t h r m {i n f}}$ -cohomology, Part II 86

Relative $\(v a r p h i, G a m m a \)$ -modules and $p$ -adic differential equations 86

A relative Langlands dual realization of $T^{\*} \(G / K \)$ and derived Satake 86

Mirror Counts of Spectral Curves 85

Optimal Spectral Lower Bounds and Nonradial Nonlinear Asymptotic Stability of a Family of Three-Dimensional Keller--Segel Self-Similar Blow-Up Solutions 85

Kobayashi Hyperbolicity of General Surfaces via the Poincar\'e Problem 85

Cohomological Hall algebras and Quot schemes of curves 85

2026-09-10 ​

The sphere packing problem in dimension 24 95 ​

Algorithmic List Decoding of Reed-Solomon Codes up to Capacity 95 ​

The maximum relaxation time of a random walk on regular graphs 92 ​

Two global stability theorems for small-data 3D compressible Euler solutions: Unique maximal globally hyperbolic developments with gradient-blowup & smooth global existence in the entire spacetime 88 ​

A sharp version of Talagrand's selector process conjecture, with applications to rounding fractional covers and Bernoulli Sudakov minoration 88 ​

Exact Asymptotics for the 2D Euclidean Random Matching Problem 88 ​

Solution of uniform Tur\'an's Tetrahedron Problem 88 ​

Monodromy Eigenvalues of Milnor Fibers for Line Arrangements 86 ​

Logarithmic A_{mathrm{inf}}-cohomology, Part II 86 ​

Relative \(varphi,Gamma\)-modules and p-adic differential equations 86 ​

A relative Langlands dual realization of T\*\(G/K\) and derived Satake 86 ​

Mirror Counts of Spectral Curves 85 ​

Optimal Spectral Lower Bounds and Nonradial Nonlinear Asymptotic Stability of a Family of Three-Dimensional Keller--Segel Self-Similar Blow-Up Solutions 85 ​

Kobayashi Hyperbolicity of General Surfaces via the Poincar\'e Problem 85 ​

Cohomological Hall algebras and Quot schemes of curves 85 ​

2026-09-10

The sphere packing problem in dimension 24 95

Algorithmic List Decoding of Reed-Solomon Codes up to Capacity 95

The maximum relaxation time of a random walk on regular graphs 92

Two global stability theorems for small-data $3 D$ compressible Euler solutions: Unique maximal globally hyperbolic developments with gradient-blowup & smooth global existence in the entire spacetime 88

A sharp version of Talagrand's selector process conjecture, with applications to rounding fractional covers and Bernoulli Sudakov minoration 88

Exact Asymptotics for the 2D Euclidean Random Matching Problem 88

Solution of uniform Tur\'an's Tetrahedron Problem 88

Monodromy Eigenvalues of Milnor Fibers for Line Arrangements 86

Logarithmic $A_{m a t h r m {i n f}}$ -cohomology, Part II 86

Relative $\(v a r p h i, G a m m a \)$ -modules and $p$ -adic differential equations 86

A relative Langlands dual realization of $T^{\*} \(G / K \)$ and derived Satake 86

Mirror Counts of Spectral Curves 85

Optimal Spectral Lower Bounds and Nonradial Nonlinear Asymptotic Stability of a Family of Three-Dimensional Keller--Segel Self-Similar Blow-Up Solutions 85

Kobayashi Hyperbolicity of General Surfaces via the Poincar\'e Problem 85

Cohomological Hall algebras and Quot schemes of curves 85