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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars： Liouville theorems for superlinear parabolic problems
超线性 抛物线问题 刘维尔定理
2023/4/23
We first consider positive classical solutions to a semilinear heat equation and discuss the associated Liouville-type theorems and their consequences on a priori estimates of solutions (in particular...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Supercongruences involving Motzkin numbers and central trinomial coefficients
莫茨金数 中心三项式系数 超同余
2023/4/21
In this talk, we investigate congruence properties for Motzkin numbers and central trinomial coefficients. Let M_n and T_n denote the nth Motzkin number and the nth central trinomial coefficient respe...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Some conjectures on real-rootedness
实根性 组合数学 大群多项式
2023/4/21
The real-rootedness has been drawing attention of many mathematicians to study them on a large group of polynomials in Combinatorics. This talk is concerned with some conjectures on the real-rootednes...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Space-time finite and boundary element methods for the wave equation
波动方程 时空有限元 边界元方法
2023/4/21
In this talk we will review some recent results on space-time finite and boundary element methods for the wave equation. As a first model problem we consider the inhomogeneous wave equation with zero ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The logarithmic Brunn-Minkowski inequality conjecture in convex geometry
凸几何 对数 布伦-闵可夫斯基 不等式猜想
2023/4/21
The logarithmic Brunn-Minkowski inequality conjecture is one of the most intriguing challenges in convex geometry since 2012. Notably, this conjectured inequality is stronger than the celebrated Brunn...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On the Riemann-Hilbert problem of confluent hypergeometric systems and Seiberg-Witten curves
超几何系统 塞伯格-维滕曲线 黎曼-希尔伯特问题
2023/4/21
This talk first solves explicitly a Riemann-Hilbert problem of confluent hypergeometric systems. It then conjectures and proves a special case that the WKB approximation of the monodromy data of confl...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Recent developments on random hyperbolic surfaces of large genus
大属随机 双曲曲面 球面几何
2023/4/21
In this talk, we report several very recent asymptotic results on certain classical geometric quantities viewed as random variables on the moduli space of Riemann surfaces for large genus (and many cu...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Global stability of the Minkowski spacetime for the Einstein-Vlasov system
爱因斯坦-弗拉索夫系统 闵可夫斯基时空 全球稳定性
2023/4/21
In this talk, we discuss the global stability of the Minkowski spacetime in the wave coordinates system for the massive Einstein-Vlasov system. In particular, compared with previous results by Lindbla...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Kolmogorov-Smirnov type testing for structural breaks: A new adjusted-range based self-normalization approach
结构断裂 Kolmogorov-Smirnov检验 KS检验 调整范围 自归一化方法
2023/4/23
A popular self-normalization (SN) approach in time series analysis uses the variance of a partial sum as a self-normalizer. This is known to be sensitive to irregularities such as persistent autocorre...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Bergman reproducing kernels for nearly holomorphic functions on bounded symmetric domains
伯格曼 有界对称域 近乎全纯函数 核
2023/4/17
Nearly holomorphic functions on symmetric domains are defined by Shimura as polynomial of differential of Kaehler potential with holomorphic coefficients. We find the corresponding Bergman reproducing...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars： Bergman reproducing kernels for nearly holomorphic functions on bounded symmetric domains
伯格曼 有界对称域 近乎全纯函数 核
2023/4/23
Nearly holomorphic functions on symmetric domains are defined by Shimura as polynomial of differential of Kaehler potential with holomorphic coefficients. We find the corresponding Bergman reproducing...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Differentiability of volume functions for big classes
大类 体积函数 可微性
2023/4/17
We report a recent paper of Witt Nystrom, where he proved the differentiability of volume functions using deformation to the normal cone.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Structured Matrices Approach for Legendre Pairs
勒让德对 结构化 矩阵方法
2023/4/17
Legendre Pairs are combinatorial objects with a rich 20+ years history. Their main application is that they furnish a structured form of the Hadamard conjecture and they have been studied by several a...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Rational points and homogeneous spaces over function fields of curves
曲线函数场 有理点 齐次空间
2023/4/17
In the last decade, there has been a growing interest in the study of rational points on homogeneous spaces of linear algebraic groups defined over fields having good arithmetical properties other tha...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：地缘政治风险与全球价值链：脆弱性测度与反事实模拟
地缘政治风险 全球价值链 脆弱性测度 反事实模拟
2023/4/17
近些年频发的地缘政治冲突及潜在的价值观同盟体系建设正在破坏高效运行、紧密依存的全球价值链分工网络。本文定义了全球价值链脆弱性概念，构建了经济体（部门）层面的全球价值链脆弱性指标和双边层面的相对脆弱性指标，探究了当前地缘政治风险对各经济体（部门）全球价值链脆弱性的放大作用。实证研究发现，考虑地缘政治风险后，经济体参与全球价值链的脆弱性表现出不同程度的放大，其中作用于美国与部分对美依赖较高的经济体的"...