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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On a Bogomolov type vanishing theorem
Bogomolov型 消失定理 代数几何
2023/11/29
The Bogomolv theorem holds great importance in algebraic geometry, particularly in the field of birational geometry. During this presentation, we will introduce our recent work on a variant of the Bog...
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：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：t-stabilities and t-structures for the weighted projective line of type (2)
加权投影线 t-稳定性 t-结构
2023/11/13
We focus on the study of t-stabilities on a triangulated category in the sense of Gorodentsev, Kuleshov and Rudakov. We give an equivalent description for the nest t-stabilities on certain triangulate...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The study of derived representation type via topological and homological methods
拓扑 同调 派生表示类型
2023/11/13
In these two talks, some results on derived representation type via topological and homological methods will be introduced: (1) Two geometric models for graded skew-gentle algebras will be introduced ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Numerical simulation and optimal design of fissure karst type high-temperature thermal storage and development
裂隙岩溶型 高温储热开发 数值模拟 优化设计
2023/11/6
我国中低温地热直接利用世界第1，包括温泉洗浴、空间供暖等；高温地热资源储量虽然丰富，但其发电仅排世界第18，利用率不高。裂隙岩溶型地热资源作为主要高温地热资源类型，我国隐伏碳酸盐岩面积达250万平方公里以上，初步估算0-3km深度区间的热能量相当于5000-50000亿吨标煤，雄安是典型地区；同时，我国油气伴生缝洞型地热资源丰富，具有埋藏深、温度高的特点。对此，基于离散缝洞网络模型，形成了考虑渗流...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Integral equations with bubble-type kernel via the method of moving spheres
运动球体 气泡型核 积分方程
2023/4/27
In this talk, I will describe a moving sphere approach to a class of integral equations with bubble-type kernel. This class of equations comes from higher-order elliptic equations on the standard sphe...
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：Entropy-Dissipation Informed Neural Networks for McKean-Vlasov type PDEs
McKean-Vlasov型 偏微分方程 熵耗散 信息神经网络
2023/4/13
We extend the concept of self-consistency for the Fokker-Planck equation (FPE) [Shen et al., 2022] to the more general McKean-Vlasov equation (MVE). While FPE describes the macroscopic behavior of par...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A Liouville’s theorem for some Monge-Ampère type equations
蒙日-安培型方程 刘维尔定理 单调准局部质量类型量
2023/4/13
We study a Monge-Ampère type equation which interpolates the sigma_2-Yamabe equation in conformal geometry and the 2-Hessian equation. In dimension 4, we prove a corresponding Liouville’s theorem. Our...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Barron Type Spaces in Neural Network Approximation
神经网络 巴伦类型空间 经典函数空间
2023/4/13
We shall discuss various Barron type spaces arising from neural networks. The relations among these spaces will be clarified, and we shall also establish the relationship between Barron type spaces an...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Heintze Karcher type inequalities on capillary hypersurfaces in hyperbolic space
双曲空间 毛细管超表面 海因茨·卡彻型不等式
2023/4/23
In this talk, I will introduce our recent result on Heintze Karcher type inequalities for capillary hypersurfaces supported on different types of umbilical hypersurfaces in hyperbolic space. I will in...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On nonlinear Schrodinger-type equations with nonlinear damping
非线性阻尼 非线性 薛定谔型方程
2023/4/25
In this talk，I will introduce equations of nonlinear Schrodinger-type augmented by nonlinear damping terms. The nonlinear damping can prevent finite time blow-up in several situations. The solution of...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A unified method to construct soliton solutions to NLS type equations by the KP-Toda reduction approach: Part I continuous case
KP-户田约简法 NLS类型 方程孤子解 统一方法 离散情况
2023/4/27
In these two talks, I will present a unified method to construct soliton solutions to NLS type equations by the KP-Toda reduction approach. I will take the NLS equation as a typical example and show h...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On varieties of general type with many global forms
全局形式 一般类型 品种
2023/5/6
We expect that the study of pluricanonical systems of varieties of general type with many global forms can be reduced to the study of pluricanonical systems of varieties of lower dimensions. We show t...