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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Smoothing invariant is equivalent to harmonic
平滑不变 等价 谐波 调和函数
2023/4/23
It is well known that harmonic function is smoothing invariant when convolved with the standard mollifier, which gives a quick proof of the smoothness of the harmonic function. In this talk, we will c...
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： 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：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：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：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：On the residual Monge-Ampère mass of plurisubharmonic functions with symmetry
对称性 多次调和函数 残余 蒙日-安培质量
2023/4/13
In this talk, we will study the residual Monge-Ampère mass of a plurisubharmonic function with isolated singularity at the origin in C2. We proved that the residual mass is zero if its Lelong number i...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Sharp Lp estimates and size of nodal sets of generalized Steklov eigenfunctions
Steklov-eigenfunctions 尖锐 Lp 估计 节点集
2023/4/13
We prove sharp Lp estimates for the Steklov eigenfunctions on compact manifolds with boundary in terms of their L2 norms on the boundary. We prove it by establishing Lp bounds for the harmonic extensi...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Conformally invariant fields out of Brownian loop soups
布朗环汤 共形 不变场 布朗分布
2023/4/14
For each central charge c\in (0,1], we construct a conformally invariant field which is a measurable function of the local time field \mathcal{L} of the Brownian loop soup with intensity c and i.i.d. ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Some Exact Formulas of the KPZ Fixed Point and Directed Landscape
KPZ不动点 定向景观 精确公式
2023/4/18
In the past twenty years, there have been huge developments in the study of the Kardar-Parisi-Zhang (KPZ) universality class, which is a broad class of physical and probabilistic models including one-...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Monotonicity of the second Neumann eigenfunction in symmetry domain
对称域 第二个 诺依曼特征函数 单调性
2023/4/18
In 1974, Jeffrey Rauch proposed the hot spot conjecture for the second eigenfunctions of the Neumann eigenvalue problems. We will recall some of its development and related studies in recent years. We...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：具有特殊和乐群黎曼流形中的极小子流形的形变
乐群 黎曼流形 极小子流形 形变
2023/4/18
在微分几何中，和乐群描述了向量沿闭曲线平移后与原向量的差别，反映了黎曼流形的整体微分几何性质。Berger对黎曼流形可能的和乐群进行了分类。特殊特殊和乐群黎曼流形是不同于SO(n)的可定向黎曼流形，包括Calabi-丘流形、超Kahler流形、G2流形和Spin(7)流形。这些特殊特殊和乐群黎曼流形本身具有极其丰富的结构，与多个数学分支产生深刻的联系，并且在物理上也非常重要。在此报告中，我们将介绍...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：矩形钉子，拉格朗日子流形和奇点
矩形钉子 拉格朗日 子流形 奇点
2023/4/18
2020年Greene和Lobb利用复二维空间的拉格朗日子流形分类简洁地解决了光滑约当曲线的矩形钉子存在性问题。我们将以此为引，从定性和定量两个角度介绍拉格朗日子流形分类的进展，应用和问题。
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Convergence analysis of one-point large deviations rate functions of numerical methods for stochastic wave equations with small noise
小噪声 随机波动方程 数值方法 单点大偏差率 函数收敛分析
2023/4/21
In this talk, we present the pointwise convergence of one-point large deviations rate functions (LDRFs) of the spatial finite difference method and further the fully discrete method based on the tempo...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Global quasineutral Euler limit for the Vlasov-Poisson-Landau system with rarefaction waves
稀薄波 弗拉索夫-泊松-朗道系统 准中性 欧拉极限
2023/4/24
The formal limit of the one-dimensional Vlasov-Poisson-Landau (VPL) system in the combined small Knudsen and quasineutral regimes gives the compressible Euler system. In the talk I will present a rece...