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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Prescribing sigma-2 curvature and boundary mean curvature on compact manifolds
紧致流形 sigma-2曲率 边界平均曲率
2023/11/15
On a smooth compact manifold of dimensions three and four with totally non-umbilic boundary，imposing non-negativity assumptions on curvatures of the background metric, we establish that there exists a...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Weak values as statistical estimation
统计估计 弱值 量子可观测值 最小方差
2023/11/15
Given a quantum observable and a state, one can construct a classical observable, such that it is the optimal estimate of the quantum observable, in the sense of minimum variance. We demonstrate how t...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Toric Algebras and Matroids
Toric代数 拟阵 复曲面代数
2023/11/13
In the first lecture I will give an introduction to toric algebras. A toric algebra can be seen as a monomial subalgebra, or as a quotient of a polynomial ring by a binomial prime ideal. We will discu...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On several bi-Hamiltonian systems
双哈密顿系统 齐次Hamitionan算子 相容三元组
2023/11/13
Recently, based on the classification of the second and third order homogeneous Hamitionan operators Lorenzoni and his collaborators classified compatible trios of two-component homogeneous Hamiltonia...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Integrability and constructions of the peakon systems
peakon系统 可积性 构造 Camassa-Holm方程
2023/11/13
Since the discovery of Camassa-Holm equation, because of the special properties that peakon gets, it has received considerable attention in modern Mathematics and Physics. Many new integrable dynamic ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Long-time asymptotics of soliton equations via the nonlinear steepest descent method
非线性 最速下降法 孤立子方程 长时间渐近性
2023/11/13
Based on the matrix block technique, the Deift-Zhou nonlinear steepest descent method is developed in order to study the asymptotic analysis of solutions of some nonlinear evolution equations associat...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Rigidity results in mapping class groups and homeomorphism groups
映射类群 同胚群 刚性结果
2023/11/13
Mapping class groups and homeomorphism groups are symmetry groups of surfaces and all manifolds. They are usually very rigid, in the sense that their automorphism groups only consist of conjugation. I...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Multiple solutions for a Kirchhoff-type fractional coupled problem with p-Laplacian
p-Laplacian算子 Kirchhoff型分数 耦合问题 多重解
2023/11/13
We discuss a class of two-parameters coupled Kirchhoff-type fractional differential equations. Two differentiated methods are used to prove the existence of two solutions to the equation. The fundamen...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：An inverse Lax-Wendroff procedure for finite difference schemes on the Cartesian grids
笛卡尔网格 有限差分格式 Lax-Wendroff逆过程
2023/11/13
In this talk, we introduce the so-called inverse Lax-Wendroff (ILW) boundary treatment for finite difference approximations on the Cartesian mesh. As the domain boundary may intersect with the grid in...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Higher-order Hamiltonian generalization evolution equations
高阶 哈密顿 广义演化方程
2023/11/13
In this talk, I will review several classes of higher-order generalizations of the integrable Camassa-Holm equation in the Hamiltonian forms. Then, I talk about some new results for one generalized Ca...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：New revival phenomena for bidirectional dispersive hyperbolic equations
双向离散 双曲型方程 新复活现象
2023/11/13
In this talk, the dispersive revival and fractalization phenomena for bidirectional dispersive equations on a bounded interval subject to periodic boundary conditions and discontinuous initial profile...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：VC-PINN: variable coefficient physics-informed neural network for forward and inverse problems of PDEs with variable coefficient
VC-PINN 变系数 偏微分方程 正逆问题 变系数物理 知情神经网络
2023/11/13
The talk proposes a deep learning method specifically dealing with the forward and inverse problem of variable coefficient partial differential equations-Variable Coefficient Physics-Informed Neural N...
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：Positivity and model complete fields
正性 模型完备域 有理数域
2023/11/13
In recent work with Will Johnson, we have shown that given a curve C over the rational number field Q with genus at least 2 and C(Q) is empty, the class of fields K of characteristic 0 such that C(K) ...
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
2023/11/13
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.