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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Top-heaviness of lower Bruhat intervals
较低 Bruhat区间 顶部厚重感
2023/11/13
Bjorner and Ekedahl (Ann. of math., 2008) proved that lower Bruhat intervals of crystallographic Coxeter groups are top-heavy using Hodge theory. Using Soergel bimodules and their Hodge theory establi...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On the Gauss maps of complete minimal surfaces in Rm
Rm 完全极小曲面 高斯映射
2023/12/11
We prove that if the Gauss map of a minimal surface immersed in Rm omits a generic hypersurface of large enough degree, then it must be constant.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars： The C0 estimate of the cscK equation
cscK方程 C0估计 ABP最大值原理
2023/12/11
We report the work of Chen-Cheng on the existence of cscK metrics. In this talk I will mainly focus on the C0 estimate, which is derived using the ABP maximum principle.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Asymptotic log-concavity of dominant lower Bruhat intervals
显性 Bruhat区间 渐近对数凹性
2023/11/13
The unimodality of lower Bruhat intervals for the “upper half” remains as an open problem. For affine Weyl group W with corresponding finite Weyl group W_f, we prove that lower W_f-parabolic Bruhat in...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Convergence of the Planewave Approximations for Incommensurate Systems
不可测系统 平面波逼近 收敛性
2023/12/11
Incommensurate structures come from stacking the single layers of low-dimensional materials on top of one another with misalignment such as a twist in orientation. While these structures are of signif...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：P-adic Simpson correspondence via exponential twisting
指数扭曲 P—adic—Simpson对应 p-adic-Simpson对应关系
2023/12/11
In this talk, I shall explain the work of G. Faltings on a p-adic Simpson correspondence, using exponential twisting. This reinterpretation of the correspondence makes clearer analogy between the p-ad...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Recent progress on steady Prandtl equation and Tollmien-Schlichting waves
稳定 Prandtl方程 Tollmien-Schlichting波
2023/11/9
The Prandtl equation introduced by Prandtl in 1904 is a basic equation describling the behavior of the fluid near the boundary at high Reynolds number regime. In this talk, I will first introduce some...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Linear Programming on the Stiefel Manifold
Stiefel流形 线性规划 线性函数
2023/12/11
我们研究Stiefel流形上线性规划(LPS)：其目标是线性函数，变量是p个n维空间正交向量（即Stiefel流形约束,p<=n），额外再满足k个线性约束。据我们所知，该模型首次被研究。k=0的(LPS)是一个经典的多项式可解问题。
刘徽实验室揭牌仪式暨首届数学与应用研讨会成功举行（图）
刘徽实验室 揭牌仪式 数学与应用研讨会
2024/1/11
2023年10月30日，刘徽实验室揭牌仪式暨首届数学与应用研讨会在香港中文大学（深圳）成功举行。中国科学院数学与系统科学研究院副院长、中国科学院院士张平，香港中文大学（深圳）副校长、中国工程院（外籍）院士罗智泉，深圳市大数据研究院副院长蔡小强，刘徽实验室主任、中国科学院数学与系统科学研究院袁亚湘院士，刘徽实验室学术委员会主任、中国科学院数学与系统科学研究院马志明院士等出席本次活动，共同见证了这一学...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A 1.344-approximation algorithm for the vertex cover problem
顶点覆盖问题 1.344 近似算法
2023/12/11
We present an algorithm for the vertex cover problem by combining the LP relaxation and the random edge-reductions. The algorithm has the expected approximation ratio of 1.344.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Statistical Management Theory for Business Applications with Massive Scale
大规模 商业应用 统计管理
2023/12/11
这是一个大数据与人工智能的时代，催生了各种各样大规模商务新场景。新场景常常呈现出：大规模、大数据、大模型的特点。这些特点对统计学的理论与计算方法都提出了新挑战，也提供了新机遇。对此，我将通过三个具体的真实案例分享，希望从中能够总结典型的统计学科学问题，洞察未来可能的研究机遇。这三个案例分别来自：金融科技、视频直播、和智慧零售三个不同商务场景。其中科技金融案例将展示如何通过二维码聚合支付数据助力面向...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：t-stabilities and t-structures for the weighted projective line of type (2)
加权投影线 t-稳定性 t-结构
2023/11/13
We focus on the study of t-stabilities on a triangulated category in the sense of Gorodentsev, Kuleshov and Rudakov. We give an equivalent description for the nest t-stabilities on certain triangulate...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Recent progress on holomorphic Morse inequalities
全纯 Morse不等式 CR流形
2023/11/13
In this talk, we present recent progress on holomorphic Morse inequalities. We first review the history and motivation. Then we introduce recent results on CR manifolds. Finally we give a uniform proo...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Introduction to Bourguignon-Gauduchon's variation formula for Dirac operators
Dirac算子 Bourguignon-Gauduchon 变分公式
2023/11/13
我们将介绍由Bar-Gauduchon-Moroianu给出的spin流形上Dirac算子在度量变化时一阶变分公式的证明。作为应用，我们将计算Dirac算子沿Ricci flow的一阶变分。
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A link invariant from higher-dimensional Heegaard Floer homology
高维 Heegaard-Floer同调 链接不变量
2023/11/13
We define a higher-dimensional analogue of symplectic Khovanov homology. Consider the standard Lefschetz fibration of a 2n-dimensional Milnor fiber of the A_{k-1} singularity. We represent a link by a...