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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On the Pleijel identity
Pleijel恒等式 光滑边界 Blaschke–Petkantschin
2023/10/16
Let K be a planar convex body with C^1 boundary. Consider a random line G intersecting K. In [1] Pleijel discovered an identity expressing the integral functional of the length of the chord G ∩ K in t...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Ambartzumian combinatorial formula and its applications
Ambartzumian 组合公式 有限线段集
2023/11/6
Consider a finite set of segments on a plane with endpoints in the general position. In [1] Sylvester posted a problem of finding the measure of the set of lines intersecting all of this segments. In ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Mixed volume of infinite-dimensional convex compact sets II
无限维 凸紧集 混合体积
2023/11/6
Using the results presented in the previous lecture, namely the generalization of the Tsirelson's theorem [2] to mixed volumes, we calculate the mixed volume of the closed convex hulls of the two orth...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Mixed volume of infinite-dimensional convex compact sets I
无限维 凸紧集 混合体积
2023/11/6
Let K be a convex compact subset of a separable Hilbert space H. One of the most important geometric characteristics of K is its intrinsic volumes. In the finitedimensionalcase (K ? R^d), the intrinsi...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：An algebraic framework for geometrically continuous splines
几何 连续样条 代数框架
2023/11/6
Geometrically continuous splines are piecewise polynomials defined on a collection of patches stitched together through transition maps. In this talk, we introduce an algebraic framework to study geom...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：3D Fracture Development Analysis with A Modified XFEM
XFEM 三维裂缝 发育分析
2023/11/6
扩展有限元法(XFEM)是目前裂纹分析的主流数值方法。2009年起，ABAQUS、ANSYS等主流商业软件集成XFEM并应用于裂纹问题，标志着该方法被工业界广泛接受。然而，在实际应用中XFEM仍然受到两方面的困扰：总体方程高度病态和动力学计算时能量难以守恒。基于“困难的根源在于单位分解插值引入的额外自由度”这一判断和认识，我们提出了一种无额外自由度的改进型扩展有限元方法，有效解决了现有方法总体刚度...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：近可积哈密尔顿系统辛算法的KAM定理
近可积 哈密尔顿系统 辛算法 KAM定理
2023/11/6
本报告讨论Hamilton系统辛算法的KAM稳定性，给出辛算法应用于近可积系统时不变环面的存在性证明和数值逼近结果。具体地，近可积系统用辛算法离散化，假设系统的可积部分满足Ruessmann非退化条件，当时间步长足够小且Hamilton函数足够光滑时，离散系统存在不变环面，它们在相应空间中占据一个大测度Cantor集。进而假设系统的可积部分满足Kolmogorov非退化条件，则在Hausdorff...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Some Results on Partial Inverse Spanning Tree Problems
部分逆生成树 有权函数 非循环边子集
2023/11/6
Given a graph G with weight function w and an acyclic edge subset E', the partial inverse spanning tree problem on (G, w; E') is to find a new weight function w* so that E' can be extended to a maximu...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Characterizations of Separably Differentially Closed Fields
可分 微分闭域 微分场
2023/11/7
In this talk, we define a new class of differential fields called separably differentially closed fields and show their several characterizations by comparing them with differentially closed fields of...
Minicourse——Purity of Brauer groups: application of perfectoids
北大 Purity of Brauer groups application of perfectoids
2023/6/16
Grothendieck predicted that the cohomological Brauer group of a regular scheme X is insensitive to removing a closed subscheme Z of X of codimension>=2. By Gabber's several results, the conjecture was...
On the Interplay Between Deep Learning and Dynamical Systems
Deep Learning Dynamical Systems 北大
2023/6/16
The explosion of spatiotemporal data in the physical world requires new deep learning tools to model complex dynamical systems.
School Colloquium——Stable reduction of algebraic curves and abelian varieties
北大 algebraic curves abelian varieties
2023/6/16
The stable reduction theorem was proved by Grothendieck for Abelian varieties and subsequently by Deligne and Mumford for projective curves.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Mixing flow and advection-diffusion-reaction equations
混合流 平流 扩散反应方程
2023/5/18
In the study of incompressible fluid, one fundamental phenomenon that arises in a wide variety of application is dissipation enhancement by so-called mixing flow. In this talk, I will give a brief int...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Almost sure scattering for the cubic NLS on R3T1
R3T1 三次NLS 散射 Cauchy问题
2023/5/18
We consider the Cauchy problem for the defocusing cubic NLS on R3T1 and establish almost sure scattering for random initial data. The main obstacle to extend the classical almost sure scattering resul...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Morse boundaries of Groups
群 Morse边界 群论
2023/5/17
The Morse boundary of a proper geodesic metric space is a generalization of the Gromov boundary of a hyperbolic space. It is a quasi-isometry invariant to study "hyperbolic directions" in the space. T...