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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Guo-Jacquet 相对迹公式简介
相对朗兰兹纲领 相对迹公式 Guo-Jacquet
2023/4/23
相对朗兰兹纲领的目标之一是建立自守形式的周期积分（分析对象）与自守 L 函数的特殊值（算术对象）之间的联系。其中一个著名的例子是 Waldspurger 公式，其后被 Jacquet 用比较相对迹公式的办法重新证明。在本报告中，我们打算介绍 Guo-Jacquet 猜想的 Waldspurger 定理的一种高维推广以及用于研究该猜想的相对迹公式。我们将回顾相关背景，概述已知结果，解释其中难点，并讨...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Reciprocity with Uncertainty About Others
互惠 对他人 不确定性
2023/4/21
We introduce the uncertainty of psychological motivation into a reciprocity model and explore its implications on behavior. More precisely, we assume that reciprocity sensitivities are subject to inco...
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
2023/4/21
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： 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：Improved error estimates of the splitting methods for the long-time dynamics for the weakly nonlinear Schrodinger equations
弱非线性薛定谔方程 长时间动力学 分裂方法 误差估计
2023/4/21
We establish improved uniform error bounds for the time-splitting methods for the long-time dynamics of the nonlinear Schr\"odinger equation (NLSE) with weak nonlinearity. By a new technique of regula...
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：Dynamics of multi-solitons to Klein-Gordon equations
多孤子 克莱因-戈登方程 动力学
2023/4/21
I will report my recent joint work with Jacek Jendrej on muti-solitons to the Klein-Gordon equations including their asymptotic stability and classification.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Robust Formation Control for Heterogeneous Multi-Agent Systems
异构 多智能体系统 稳健化成控制
2023/4/21
The coordination control problems for heterogeneous multi-agent systems (MASs) have received considerable interests such as consensus, synchronization, distributed formation control. In this presentat...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：基于斜率压缩因子的高精度紧致气体动理学格式
斜率压缩因子 高精度 气体动理学格式
2023/4/19
本报告将结合团队多年来在高精度方法的研究基础，围绕高精度方法的三维高超声速复杂绕流模拟瓶颈问题，详细介绍有限体积框架的假设和限制、时空耦合紧致气体动理学格式（CGKS）的构成、斜率压缩因子突破有限体积方法单元内部连续性假设的原理以及团队在CGKS方面的最新研究成果，为高超声速飞行器的高精度模拟应用提供参考。
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：差分隐私分布式控制
差分隐私 分布式 控制
2023/4/21
本文研究了符号网络上的差分隐私二部一致性问题。针对这一问题，提出了一种在合作竞争交互信息中加入时变方差噪声的新算法。为了实现隐私保护，允许增加附加噪声的方差，这与现有的文献有本质的不同。此外，添加噪声的方差可以是衰减的或恒定的。通过使用基于随机逼近方法的时变步长，我们证明了该算法均方意义下收敛，并且即使在隐私噪声增加的情况下也几乎处处收敛。我们进一步提出了了一种设计步长和噪声参数的方法，使得算法在...