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03
2026/04
Moments and Asymptotic Normality for Random Strict (n, dn ± 1)-Core Partitions
Amdeberhan's conjectures concerning the enumeration, average size, and largest size of strict $(n,n+1)$-core partitions have stimulated extensive research in this area. Nevertheless, the investigation of random core partitions remains relatively underdeveloped. In this talk, we first present several polynomiality results and asymptotic formulas for the moments of sizes of random strict $(n, dn\pm 1)$-core partitions. We further establish the asymptotic normality of their sizes. Analogous results are also derived for random (strict) $n$-core partitions and random self-conjugate $n$-core partitions with bounded perimeters. These findings resolve several conjectures posed by Zaleski and stand in contrast to the asymptotic behavior derived by Even-Zohar in 2022 for the size of a random $(s,t)$-core partition with coprime $s$ and $t$, which converges in distribution to Watson’s $U^2$ distribution. These are joint works with Wenston J.T. Zang, Yetong Sha, and Jiange Li.
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01
2026/04
Expansion coefficients of the first order Melnikov functions near polycycles with hyperbolic saddles
Under a suitable assumption we obtain all expansion coefficients and their analytical relation for the first order Melnikov function near a polycycle with hyperbolic saddles. As an application we consider heteroclinic bifurcations for a φ-Laplacian Liénard system and give the number of limit cycles bifurcated from the heteroclinic loop.
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01
2026/04
Equivariant Kazhdan-Lusztig Polynomials of Thagomizer Matroids under the Action of the Hyperoctahedral Group
For each integer $n\ge 1$, the thagomizer matroid is the graphic matroid of the complete tripartite graph $K_{1,1,n}$ (with parts of sizes $1,1,n$); for $n\ge 2$, its full automorphism group is the hyperoctahedral group. We compute the Kazhdan--Lusztig polynomial and the inverse Kazhdan--Lusztig polynomial in the equivariant setting for this action, and we show that each coefficient is an honest representation with a multiplicity-free irreducible decomposition. Taking dimensions recovers the previously known nonequivariant thagomizer polynomials, and the coefficient formulas are naturally stated using the wreath product Frobenius characteristic for the hyperoctahedral group.
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01
2026/04
Positivity in the Kazhdan-Lusztig-Stanley Theory for Matroids
We will survey recent developments in the positivity of the matroid Kazhdan–Lusztig–Stanley theory. Elias, Proudfoot, and Wakefield introduced the matroid Kazhdan–Lusztig polynomial and posed two conjectures: nonnegativity and log-concavity. While the nonnegativity conjecture has been proved, log-concavity remains a central open problem. This talk reviews current progress on some invariants: the (inverse) Kazhdan–Lusztig polynomials and the (inverse) Z-polynomials. We will outline the latest results and open questions concerning their unimodality and log-concavity. Finally, we will present our recent contributions as follows: log-concavity of inverse Kazhdan–Lusztig polynomials for paving matroids;log-concavity of inverse Z-polynomials for sparse paving matroids; unimodality of Kazhdan–Lusztig polynomials for sparse paving matroids.This is joint work with Alice L. L. Gao, Yun Li, Philip B. Zhang, and Zuo-ru Zhang.
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31
2026/03
法学学科建设的创新路径与论文发表
聚焦法学学科如何通过交叉融合实现创新发展，并针对核心期刊论文发表，强调从问题意识、论证规范到投稿策略的全流程方法论，从而提升法学研究的质量与学术影响力。
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30
2026/03
新质生产力专门立法的基础与超越——以PDA（平台、数据、算法）为视角
一、引言：新质生产力对法治范式提出的挑战二、解码PDA：新质生产力的“新”在何处三、专门立法的必要性四、超越传统路径：立法范式的创新五、从规制走向治理：PDA法律规制的三重模式
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29
2026/03
Quantum metric-based optical selection rules and induced magneto-optical effects
Quantum geometry is the source of many novel effects and new quantum states. The real and imaginary parts of the quantum geometry tensor correspond to the quantum metric and Berry curvature, respectively. Berry curvature has been well studied over the past four decades, while the exploration of quantum metric is just beginning. In this report, I will introduce some of the progress we have made in the study of quantum metric. In the first part of the report, we propose quantum metric-based optical selection rules [1]. We unveil a universal quantum metric and oscillator strength correspondence for linear polarization of light and establish valley-contrasted optical selection rules that lock orthogonal linear polarizations to distinct valleys. Part II, we propose quantum metric as a new mechanism for magneto-optical effects (MOEs) beyond the Berry curvature paradigm [2,3]. We develop new general MOE formulas that incorporate the whole quantum geometry, namely both Berry curvature and quantum metric. Based on our formulas, we predict quantum metric-induced MOEs in space-time inversion (PT)-symmetric antiferromagnets and unconventional MOEs, that is, quantum metric–dominated MOEs, in altermagnets.1.Quantum-Metric-Based Optical Selection Rules, Y. Li, and C.-C. Liu*, PRL 136, 046901 (2026).2.Quantum metric induced magneto-optical effects in PT-symmetric antiferromagnets, Y. Li, Y. Liu, C.-C. Liu*, arXiv:2503.04312v1 (2025).3.Unconventional Magneto-Optical Effects in Altermagnets, Y. Li, Y. Liu, C.-C. Liu*, arXiv:2512.03435v1 (2025).
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30
2026/03
Braid groups, Voronoi diagrams, and the Pentagon equations.
In this talk we shall define the classical braid group and a way how to get its representation by using Voronoi diagrams and Pentagon relations.Those interested in deeper understanding and further scientific questionsare recommended to read the book by V.O.Manturov and the paper by R.Penner.
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02
2026/04
88304am永利集团地理大数据计算与资源规划研究实验室2026年学术交流会暨思路沙龙?青年学者论坛
2：00 近自然恢复下全球陆地实际固碳潜力与水资源消耗权衡关系研究 韩庆功 西北农林科技大学 主讲内容：针对近自然恢复中的恢复参照及全球近自然恢复引起的固碳潜力和水资源消耗权衡关系问题，构建潜在自然植被分类模型并预测空间格局，提供恢复参照；评估未来实际恢复背景下全球陆地固碳潜力和水资源消耗，构建权衡固碳潜力和水资源消耗的恢复框架。为优化自然恢复路径及制定水资源约束下的资源高效利用策略提供科学依据。2：30 异质性地表的蒸散发遥感估算方法研究 张艺潇 武汉大学 主讲内容：蒸散发是全球水分和能量循环的关键环节，也是陆地表层水循环中最大且最难估算的分量。由于地表存在广泛的空间异质性，区域蒸散发的准确估算面临着巨大挑战。因此，我们聚焦于异质性地表的蒸散发遥感估算，通过分析蒸散发相关参量的空间异质性，明确异质性地表蒸散发产生差异的原因，进而围绕提高其估算精度开展系统研究。3：00 生态系统服务及气候干扰机制研究 樊斐斐 中科院地理所 主讲内容：本汇报围绕农林转化生态效应与旱区植被韧性两大核心研究展开。对中南半岛农林转换进行橡胶林识别与生态效应评估，系统分析其对景观格局、植被动态及生态系统服务的影响；同时揭示中国旱区植被韧性的时空格局、水分驱动机制及干旱阈值，重点关注干旱干扰下的植被响应及其对生态系统服务的调控作用。研究从土地利用变化与气候干扰的交互视角出发，为生态保护与可持续管理提供科学依据与决策参考。3：30 基于GRACE重力卫星的全球重要农业流域淡水储量变化机制及干旱缺水风险 刘梦竹 中科院农业资源研究中心 主讲内容：本次汇报以全球重要农业区的淡水储量变化机制、干旱缺水等内容展开，依据GRACE卫星总水储量、气象、灌溉用水等遥感、地面观测数据，采用全球水文、陆面模型模拟和数理统计方法，揭示了全球重要农业流域未来面临着淡水枯竭、干旱缺水加剧等风险。另外以中国的松花江流域、黄河流域为典型案例分析了水储量对流域综合管理的启示。4：00 气候变化下农业气象灾害减产风险与适应 张传伟 中国科学院大学 主讲内容：农业气象灾害是造成粮食减产的关键因素。汇报围绕“气候变化下农业气象灾害减产风险与适应”的主题，依托博士及博士后阶段的研究工作，阐述高温-干旱复合事件对东北春玉米生产的影响、风险及品种适应潜力；将尺度扩展至全国，介绍主要粮食作物在干旱、高温-干旱复合事件影响下的风险与适应研究进展；并提出未来工作计划。4：30 区域和产业可持续性转型研究 李营营 中科院南京地理与湖泊研究所 主讲内容：围绕区域与产业可持续性转型，汇报博士论文及在读期间的主要研究成果。面向国家农业绿色发展与粮食安全需求，构建农业可持续性转型分析框架，揭示长三角农业生态转型的区域分异及其形成机制。未来研究可从城乡要素流动与地域重构视角出发，探讨人口、资本与消费流动对乡村转型空间格局的塑造机制，并分析乡村旅游资源转化及其空间配置逻辑。
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02
2026/04
New error bounds for SDE-based sampling algorithms beyond log-concavity
Generating samples from a high dimensional probability distribution is a fundamental task with wide-ranging applications in the area of scientific computing, statistics and machine learning. This talk will focus on high dimensional sampling algorithms based on time discretizations of stochastic differential equations (SDEs). New error bounds will be then provided for the considered sampling algorithms without log-concavity, where the convergence rate and the dimension dependence are explicitly revealed. Numerical experiments will be finally presented to corroborate the theoretical findings.
