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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Some Applications of Nevanlinna Theory
Nevanlinna理论 指数多项式 算术性质 Green Griffiths-Lang猜想
2023/11/29
In this talk, we will introduce some applications of Nevanlinna theory to “arithmetic properties” of exponential polynomials and some special cases of Green-Griffiths-Lang conjecture with moving targe...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Modularity of WRT invariants via resurgence theory
复活理论 WRT不变量 模性
2023/11/29
We will talk about the (quantum) modularity of WRT invariants or GPPV invariants in general of Seifert fibered homology spheres. It turns out that they are related to the Stokes phenomena of the Ohtsu...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On deformation limit in deformation theory
变形理论 变形极限 射影流形
2023/11/15
This talk mainly concerns the projective, Moishezon and Kahler loci of a family. We first introduce four conjectures on this topic and then the works of the deformation limit of projective manifolds a...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Kodaira-type and Bott-type vanishings via Hodge theory
Hodge理论 Kodaira型 Bott型消失
2023/11/13
I will first give a brief introduction to T. Mochizuki's Theory of twistor D-modules. Then, we use it to study Kodaira-type vanishings. In particular, we will generalize Saito vanishing, and give a Ka...
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：Kahler geometry methods in Gaussian Gabor frame theory
高斯 Gabor框架理论 Kahler几何
2023/11/6
We investigate the frame set of regular multivariate Gaussian Gabor frames using methods from Kahler geometry such as Hormander's $\dbar$-L2 estimate with singular weight, Demailly's Calabi--Yau metho...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Arnold conjecture and advances in Floer theory
阿诺德猜想 弗洛尔理论 哈密顿微分同胚
2023/5/4
In 1960s, Arnold conjectured that the number of fixed points of a Hamiltonian diffeomorphism of a symplectic manifold should be (much) greater than its counterpart for a general diffeomorphism. This c...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Topological materials: concept, theory, prediction, and detection
拓扑材料 固体物理学 量子霍尔效应
2023/4/17
物理学中许多概念是在不断地发展中的。例如人们对光、电子等的理解与它们刚开始出现时的概念已经发生了许多进化，而固体物理学中的“绝缘体”概念也是如此。近三十年来，量子霍尔效应的相关研究不仅催生了拓扑序这一新的物相分类，也推动了拓扑绝缘体这一新兴研究领域的诞生和发展。随着量子自旋霍尔效应、拓扑晶体绝缘体等工作的后续展开，人们意识到对称性可以带来新的拓扑态，同时也不断地在“普通绝缘体”中发现新的拓扑态。这...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Ergodic Theory and Semisimple Groups
遍历理论 半简单群 马古利斯超刚性定理
2023/4/13
We go through Zimmer's book Chapter 2-3, making some preparations for Margulis super-rigidity theorem.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Random Surface, Planar Lattice Model, and Conformal Field Theory
随机曲面 平面晶格模型 共形场论
2023/4/13
Liouville quantum gravity (LQG) is a theory of random surfaces that originated from string theory. Schramm Loewner evolution (SLE) is a family of random planar curves describing scaling limits of many...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：New extreme value theory for maxima of maxima
极大值 最大值 新极值理论
2023/4/18
Although advanced statistical models have been proposed to fit complex data better, the advances of science and technology have generated more complex data, e.g., Big Data, in which existing probabili...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Richberg's extension theory
里奇伯格 扩展理论 多次调和函数扩展 卡勒几何
2023/4/18
In this talk I will recall Richberg's extension theorem of plurisubharmonic functions and discuss its application in Kahler geometry.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Periodic Phenomena in homotopy theory
同伦理论 周期现象
2023/4/25
Chromatic homotopy theory uses the algebraic geometry of smooth 1-parameter formal groups to separate stable homotopy theory into periodic layers. The 1st layer recovers the image of Adams’ J homomorp...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Dynamic Learning and Modelling of Nonlinear Spatio-Temporal Network Data: theory with an application to the EU energy markets
非线性 时空网络数据 动态学习 建模
2023/4/28
Nonlinear modelling of dynamic spatio-temporal network data is often a challenge with various issues, in particular due to irregularly observed locations and location-wide non-stationarity. In this pa...