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2024年1月26日，国家自然科学基金基础科学中心项目“流形上的几何、分析和计算”2023年项目进展暨战略发展研讨会在中国科学院数学与系统科学研究院（以下简称数学院）召开。国家自然科学基金委（以下简称基金委）党组成员、副主任江松院士、数理科学部数学处赵桂萍副处长、数理科学部综合与战略规划处陈国长副处长、数理科学部数学处王小虎项目主任，咨询专家王小云院士、张平文院士、张伟平院士，以及周向宇、郭雷、席...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Occupation fields for Markov loops
马尔可夫循环 占用域 格林函数
2023/11/29
In this talk, we introduce occupation fields for vertices and oriented edges and compute their distributions. More precisely, under the Markov loop measure, the expected number for crossings of an ori...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Nonlinear potentials at the fractional scale:sharp regularity
分数尺度 非线性势 尖锐 正则性
2023/11/29
Nonlinear potential theory and elliptic regularity theory are two classical topics in the modern analysis of partial differential equations. In this talk I show how these themes merge to solve the lon...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Adaptive stabilization of non-cooperative stochastic differential games
非合作 随机微分对策 自适应镇定
2023/11/29
We considers the adaptive stabilization problem for a basic class of linear-quadratic non-cooperative stochastic differential games when the systems matrices are unknown to the regulator and the playe...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars："Inverse problems for elliptic PDE" (7)
椭圆偏微分方程 反问题 Calderón问题
2023/11/29
This course will give an introduction to inverse problems for elliptic partial differential equations. The most famous example of such problems is the Calderón problem, which arises in seismic and med...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Laplacian estimates for the cscK equation
cscK方程 拉普拉斯估计 Nash-Moser迭代
2023/11/29
We will report Chen-Cheng’s work on cscK equations. We derive the Laplacian bound using Nash-Moser iteration.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Metric geometric aspects of Einstein manifolds
Einstein流形 度量几何 爱因斯坦流形 黎曼几何
2023/11/29
This lecture concerns the metric Riemannian geometry of Einstein manifolds, which is a central theme in modern differential geometry and is deeply connected to a large variety of fundamental problems ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars："Inverse problems for elliptic PDE" (8)
椭圆偏微分方程 反问题 Calderón问题
2023/11/29
This course will give an introduction to inverse problems for elliptic partial differential equations. The most famous example of such problems is the Calderón problem, which arises in seismic and med...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Functions of bounded variation and nonlocal functionals
有界 变差函数 非局部泛函
2023/11/29
In the past two decades, starting with the pioneering work of Bourgain, Brezis, and Mironescu, there has been widespread interest in characterizing Sobolev and BV (bounded variation) functions by mean...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars："Sobolev extensions"(7)&(8)
Sobolev扩展 Whitney扩展 技术变体
2023/11/29
I will give an introduction to Sobolev extensions, including the use of variants of the Whitney extension technique. I will concentrate on the basics of the theory.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Analytic smoothing effect of a class of ultra-parabolic equations
一类超抛物型方程 解析 光滑效应
2023/11/29
We study a class of ultra-parabolic equations, it is a high order degenerate parabolic operators of Hormander type, so it is strongly degenerate, but we prove that this class operators possesses the a...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Direct sampling method to inverse wave-number-dependent source problems: determination of the support of a stationary source
反波数 相关源问题 直接采样 固定源
2023/11/29
This talk is concerned with a direct sampling method for imaging the support of a frequency-dependent source term embedded in a homogeneous and isotropic medium. The source term is given by the Fourie...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Causal Inference based models and their applications in Banking
因果推理 模型 银行业
2023/11/29
Causal inference is a permanent challenge topic in statistics, data science, and many other applied fields. Existing machine learning methods often focus on the correlations in the data and ignore the...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Coexistence of nonempty Fatou sets and Julia sets with interior for transcendental Hénon maps
超Hénon映射 非空Fatou集 Julia集 内部共存性
2023/11/29
A Hénon map is a map of the form H(z, w) = (f(z) + aw, z). A main focus of interest are the Fatou sets and the Julia sets. In this lecture I will show that it is possible that the Fatou set and the Ju...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Some Applications of Nevanlinna Theory
Nevanlinna理论 指数多项式 算术性质 Green Griffiths-Lang猜想
2023/11/29
In this talk, we will introduce some applications of Nevanlinna theory to “arithmetic properties” of exponential polynomials and some special cases of Green-Griffiths-Lang conjecture with moving targe...