分析组大会报告人

分析组大会报告人
郭坤宇（复旦大学数学科学学院）
Title：Operator theory on the Bergman space
Abstract：In this talk, we will focus on operator theory on the Bergman space, and combine methods of complex analysis, group theory and the theory of von Neumann algebras to establish a fascinating connection between operator theory and free group factors. An interplay of analytical, geometrical, operator and group theoretical techniques is intrinsic to this work.
(1) A brief survey of von Neumann algebras;
(2)Operator theory on the Bergman space;
(3)Holomorphic coverings of planar domains;
(4)Type II factors from conformal geometry;
(5)Free group factors;
(6)Orbifold planar domains and type II factors problems, conjectures and results.
分析组邀请报告人
（1）桂贵龙（江苏大学理学院）
Title:On the global well-posedness of the 3-D inhomogeneous Navier-Stokes equations
Abstract:In this talk, we consider the local and global well-posedness of the 3-D incompressible inhomogeneous Navier-Stokes equations (INS).Without smallness assumption on the variation of the initial density function, we first prove the local well-posedness of 3-D incompressible inhomogeneous Navier-Stokes equations with initial data in the critical Besov spaces. Then we prove the global well-posedness of (INS) with highly oscillatory initial velocity field and any initial density function with a positive lower bound. On the other hand, we investigate the global well-posedness to (INS) with large initial velocity slowly varying in one space variable in the framework of anisotropic type Besov spaces.
（2）姚磊（西北大学数学系）
Title:Incompressible limit of viscous liquid-gas two-phase flow model
Abstract:We investigate the incompressible limit of the viscous liquid-gas two-phase flow model with periodic boundary conditions. It is shown that the local classical solution of the two-phase flow model converges to the local classical solution of the incompressible Navier–Stokes equations, as $\epsilon \rightarrow \infty$ which builds up the relationship between the two-phase flow model and the incompressible Navier–Stokes equations. In addition, we give the convergence rate estimates in some norms. This is a joint work with Prof. Changjiang Zhu and Dr. Ruizhao Zi
（3）邵井海（北京师范大学数学学院）
题目：随机过程的耦合及与维数无关的Harnack 不等式
摘要：
（4）夏建明（中国科学院数学与系统科学研究院）
题目：风险与不确定性厌恶
摘要：对风险与不确定性下的偏好理论及其在金融学中的应用做一简要回顾并介绍本人在相关问题上的最新进展。

（5）张希承（武汉大学数学与统计学院）
Title：$L^p$-maximal regularity of nonlocal parabolic equation and applications
Abstract：By using Fourier's transform and Fefferman-Stein's theorem, we investigate the $L^p$-maximal regularity of nonlocal parabolic and elliptic equations with singular and non-symmetric L\'evy operators, and obtain the unique strong solvability of the corresponding nonlocal parabolic and elliptic equations, where the probabilistic representation plays an important role. As a consequence, a characterization for the domain of pseudo-differential operators of L\'evy type with singular kernels is given in terms of the Bessel potential spaces. As a byproduct, we also show that a large class of non-symmetric L\'evy operators generates an analytic semigroup in $L^p$-spaces. Moreover, as applications, we prove a Krylov's estimate for stochastic differential equations driven by Cauchy processes (i.e. critical diffusion processes), and also obtain the global well-posedness to a class of fully nonlinear parabolic equation with critical diffusions. In particular, critical Hamilton-Jacobi equations and multidimensional critical Burger's equations are uniquely solvable and the smooth solutions are obtained.
（6）冀书关（吉林大学数学科学学院）
Title: Time periodic solutions of nonlinear wave equations in complex media
Abstract: This is a joint work with Prof. Yong Li. In this talk, we are concerned with the time periodic solutions of nonlinear wave equation in complex media
\begin{equation} \label{E1-1} u(x)y_{tt}-(u(x)y_x)_x+g(x,y)=f(x,t),\ x\in (0, \pi), \ t\in\mathbb{R}.
\end{equation}
By adjusting the basis of $L^2$ function space, we can circumvent the difficulties caused by the coefficients that do not meet the strong convexity, and obtain the existence of weak time periodic solution, which was posed as an open problem by Barbu etc. in 1997. Furthermore, we also present the applications to the forced Sine-Gordon equation with variable or constant coefficients.
（7）李洪全（复旦大学数学科学学院）
题目：中心极大函数范数与维数相关性的新进展
摘要：在本报告中，我们给出在各种流形上心极大函数范数与维数相关性的结果。

（8）王凯（复旦大学数学科学学院）
Title: Reducing subspaces for analytic multipliers of the Bergman space
Abstract: Several years ago some incisive results are obtained on the structures of the reducing subspaces for the multiplication operator $M_\phi$ for a finite Blaschke product $\phi$ on the Bergman space on the unit disk. In particular, the linear dimension of the commutant, $\mathcal{A}_\phi = \{M_\phi, M_\phi^*\}'$,
is shown to equal $q$, the number of connected components of the Riemann surface, $\phi^{-1} \circ \phi$. In this talk ， we will show that $\mathcal{A}_\phi$ is commutative and hence isomorphic to
\mathbb{C}^q$, and moreover, that the minimal reducing subspaces are pairwise
orthogonal and the action of $M_\phi$ on any two of them are not unitarily
equivalent. Further, the number of mutually orthogonal minimal reducing
subspaces is $q$. Finally, an analytic/arithmetic description of the minimal
reducing subspaces of $M_\phi$ is also provided, along with the taxonomy of the possible
structures of the reducing subspaces for $M_\phi$ for $\phi$ having eight zeros. These results have
implicationsin both operator theory and the geometry of finite Blaschke products. This is a joint work with Ronald G . Douglas and Mihai Putinar.
（9）陈琼蕾（北京应用物理与计算数学研究所）
Title: On the ill-posedness of the compressible Navier-Stokes equations
Abstract: We prove the ill-posedness of three dimensional compressible viscous heat-conductive flows for the initial data belonging the critical Besov space ),,(1,2/31,1/31,/3p p p p P P B B
B --+ ρ for 3>p , here ρis a positive constant. Especially, this result means that it seems impossible to construct a global solution for the highly oscillating initial velocity for the viscous heat-conductive flows. We also prove that the baratropic Navier-Stokes equation is ill-posedness for the initial data belonging to the critical Besov space ),(1,1/31,/3p p P P B B
-+ ρ for 6>p .
（10）郭紫华（北京大学数学科学学院）
Title: Harmonic analysis method in the study of KdV equation
Abstract:
（11）史少云（吉林大学数学科学学院）
Title: Galoisian obstruction to the integrability of general dynamical systems
Abstract: The Galoisian approach to study the integrability of classical Hamiltonian systems, he so-called Morales –Ramis theory, has been proved to be useful and powerful by many applications. Here, two analogous forms of the Morales –Ramis theory for general dynamical systems both in vector field and mapping forms are given. Galois groups of the corresponding variational equations are studied, and some necessary conditions of the system to possess a certain number of integrals are presented. Several applications are given at last to illustrate our results.
应用数学分组大会报告人
徐宗本（西安交通大学）
Title: 关于稀疏信息处理的几个理论问题
Abstract:
应用数学分组邀请报告人
（1）高卫国（复旦大学数学科学学院）
题目：电子结构计算中的特征值问题
摘要：密度泛函理论是研究多电子体系电子结构的量子力学方法，应用密度泛函理论多体Schr\"odinger方程可简化为Kohn-Sham 方程，相比其它简化模型应用更为普遍，其数值模拟是当今科学计算的一大挑战。

Kohn-Sham方程离散化后得到一个代数非线性特征值问题，我们将讲述这类问题的具体形式和性质，介绍数值计算方法、收敛性结果及其加速技巧，包括目前受到更多关注的线性标度算法及分析，以及各种方法在高性能计算平台包括GPU集群上的实现等.
（2）马富明（吉林大学数学科学学院）
题目：电子结构计算中的特征值问题
摘要：我们考虑一个无限界面开洞穴上的电磁散射与反散射问题。

它有很强的科学与技术背景。

问题的数学模型是Maxwell方程组于无界域上的定解问题与反问题。

我们将针对问题的难点，在数值计算中PML技术的使用、特殊形状开洞穴问题的特殊算法、反问题的数值方法等方面给出我们的研究结果。

（3）翟桥柱（西安交通大学电子与信息工程学院）
题目：具有混合动态约束的生产系统优化调度问题研究
摘要：生产系统优化调度是很多实际系统中必须解决的工程优化问题，且往往具有约束关系复杂、问题规模大等特点。

报告中将针对生产系统优化调度中的混合动态约束处理、复杂积分约束处理、大规模冗余约束快速识别等问题，介绍一些最新研究成果。

（4）杨静平（北京大学数学科学学院）
Title: Bivariate copulas' decomposition, approximation and multivariate Frechet copulas with applications in finance
Abstract:Copulas are statistical tools for modeling the multivariate dependence structure among variables in a distribution free way. Bivariate Frechet (BF) copulas characterize dependence as a mixture of three simple structures: comonotonicity, independence and countermonotonicity. In this talk, we will introduce our recent results on bivariate copulas' decomposition, approximation and multivariate Fr$\acute{\text{e}}$chet copulas in terms of BF copulas.
（5）杨瑛（清华大学数学科学系）
Title: Modeling Mixed Poisson and Continuous Longitudinal Data
Abstract:In this talk we will introduce a flexible regression models in two respects to evaluate the influence of the covariate on the mixed longitudinal Possion and continuous responses and to evaluate how the correlation between the responses changes over time. Also we discuss the joint analysis of Possion and continuous longitudinal data with nonignorable missing values under fully parametric framework.This is joint research with Jian Kang.
（6）付晓玉（四川大学数学学院）
Title:A unified theory for controllability and observability of PDEs
Abstract:This topic is devoted to a study of the controllability and observability of partial differential equations of second order. We find that, starting from a basic identity of "parabolic-like" differential operator (i.e. without elliptic condition), one can deduce all the known controllability and observability results for the parabolic, hyperbolic, Schrodinger and plate equations that are derived via Carleman estimate. Meanwhile, a new controllability and observability result is established for the complex Ginzburg-Landau equation. To some extent, we present a unified treatment on the controllability and observability problems for partial differential equations of second order.
（7）郑春雄（清华大学数学系）
Title: TBA
Abstract:
（8）靳祯（山西中北大学理学院）
题目：基于复杂网络的传染病传播动力学分析
摘要：群体水平传染病性疾病的传播一定是在特定社会网络下的病毒或者细菌的传播，其演化过程不仅依赖疾病的病原学和流行病学，而且依赖于特定网络的拓扑结构，在该报告中，我们将介绍基于不同社会网络拓扑结构特征，利用概论和统计方法，建立传染病动态网络的不同状态节点的动力学模型，并分析其演化规律；在此基础上，给出无标度社会网络下一些特定传染病高维非线性动力系统，分析基本再生数及全局稳定性，并针对实际数据进行参数估计，进而给出疾病传播的风险评估与预测。

(9)徐定华（浙江理工大学）
Title: Inverse problems of textile material design
Abstract: Textile material design is of paramount important in the study of functional clothing design. It is therefore important to reveal heat and moisture transfer characteristics in the system of human body-clothing-environment, which directly determines heat- moisture-comfort level of human body. Based on the model of steady-state or dynamic heat and moisture transfer with condensation in porous fabric under low temperature, we present new inverse problems of textile material etermination (in abbreviation IPTMD). Adopting the idea of Least Squared Method or Regularization Method, we formulate the IPTMD into a function minimization problem. By means of the numerical methods for ODEs or PDEs, quasi-solution method for inverse boundary problems and direct search methods for one-dimensional minimization problems, we construct iterative algorithms of approximated solution for the IPTMD. Theoretical study and numerical simulation results validate the formulation of the IPTMD and demonstrate effectiveness of the proposed numerical algorithms.
(10)黄建国（上海交通大学数学系）
题目：组合弹性结构问题的有限元方法
摘要：组合弹性结构由弹性体，板（壳），梁等相贯而成，广泛应用于航空、航天、舰船、土木、机械制造等领域，对它的理论分析与计算是当代结构工程、多场耦合力学和大规模科学计算等领域的交叉研究方向。

在本报告中，将讨论求解一般组合弹性结构静态问题和振动问题的有限元方法，内容涵盖算法设计、误差分析和数值模拟等。

有关结果系由报告人与陈承泽、郭玲、黄学海、赖军将、石钟慈和徐一峰等合作而得。

代数、数论、拓扑、几何分组大会报告人
宗传明（北京大学数学科学学院）
题目：神秘的四面体
摘要：四面体是三维空间中最简单的几何体之一，亚里士多德，欧几里得，阿基米德和柏拉图都曾经观察思考过它，开普勒，高斯，欧拉，希尔伯特，闵可夫斯基都曾认真研究过它。

然而，一些关于它的几何量至今未知。

例如，它的堆积密度和覆盖密度。

特别地，确定它的堆积密度是希尔伯特第十八问题的一部分，在研究这一问题的过程中，伟大的闵可夫斯基还犯过错误。

近二十年来，许多数学家，化学家，结晶学家对这一问题进行了多方位的研究。

本报告将介绍关于四面体的最新研究进展。

应用数学分组邀请报告人
（1）Bruno Ziberman
Title:Some aspects on group actions on manifolds
Abstract:
（2）田一超（中国科学院数学与系统科学研究院）
Title:Modularity lifting theorem for Hilbert modular forms in weight 1 and applications
Abstract: In 1999, Buzzard and Taylor invented the method of analytic continuation of modular forms to prove certain modularity theorem in weight 1. Their poineer work has important applications to the strong Artin conjecture for two-dimensional Galois representations over Q. In this talk, I will explain how to generalize this method to the Hilbert case. More precisely, we show that a p-adic Galois representation of a totally real field, which is residually modular and satisfies certain local conditions at p, actually comes from a holomorphic Hilbert modular form of parallel weight 1. I will explain also some applications of this result to the strong Artin conjecture over totally real field. This is a joint work with Payman Kassaei and Shu Sasaki.
（3）魏达盛（中国科学院数学与系统科学研究院）
Title:Brauer groups and Rational points
Abstract:A class of geometrically integral varieties defined over a number field $k$ satisfies Hasse principle if a variety in this class has a
$k$-rational point as soon as it has rational points in all the completions $k_v$ of the field $k$. For example, quadrics, Severi-Brauer varieties are known to satisfy this principle. However, counterexamples to Hasse Principle are also known even in the class of rational varieties. In 1970, Manin showed that an obstruction based on the Brauer group of varieties, now referred to as the Brauer-Manin obstruction, can often explain failures of Hasse principle. However, the Brauer-Manin obstruction is the only one for the existence of rational points? Some Conjectures have been given (e.g. Colliot-Thelene's conjecture) on it. In this talk, we will explain this obstruction and some known results. We will also discuss a joint work about Colliot-Thelene's conjecture (with Derenthal and Smeets).
（4）张海（西北大学数学系）
Title:社会网络结构分析
Abstract: 网络分析方法不仅提供从数据中提取信息的新方法，同时开创了数据可视化的新途径。

网络结构分析是复杂网络研究的重要课题之一，重点研究网络中社区检测问题。

Stochastic Blockmodel 是一种统计建模方法，广泛应用于网络结构分析。

但关于其研究尚缺乏统计性质分析。

我们首先研究了Stochastic Blockmodel的统计性质，给出了求解模型的最大似然估计和变分估计的渐近正态分布。

进一步，我们结合节点度信息给出了更一般的模型，并基于变分逼近的方法给出求解模型的快速算法，并应用于社会网络结构分析。

最后，我们通过相变方法研究了结点个数和组数之间的关系。

（5）杜荣（华东师范大学数学系）
题目：Strict positivity of new numerical invariants of singularities and complex Plateau problem.
摘要：We introduce some new invariants for complex manifolds. These invariants measure in some sense how far the complex manifolds are away from having global complex coordinates. As an application, we relate one of these invariants with a CR invariant to solve complex Plateau problem.
（6）黄华林（山东大学数学科学学院）
题目：张量范畴中的代数和表示论
摘要：介绍在张量范畴中如何定义代数和表示论，并据此研究量子群和张量范畴的相关问题。

（7）徐帆（清华大学数学系）
Title:On derived Hall algebras and motivic Hall algebras
Abstract: In this talk, we apply a derived analogue of the Riedtmann-Peng formula to characterize the explicit symmetries between two versions of derived Hall algebras (To\"en's version and Kontsevich-Soibelman's version) and give an alternative proof of the associativity of Kontsevich-Soibelman's motivic Hall algebras. Moreover, we construct the motivic realization of the Kac-Moody algebras and the involving integration map.
（8）叶郁（中国科技大学数学科学学院）
Title:Derivations and characteristic map of an algebra
Abstract: In this talk, I will discuss the characteristic map of an associative algebra, and give an explicit expression of the image of a derivation under the characteristic map. As an application, we show that the characteristic map of a finite dimensional path algebra is injective.
（9）韩小利（清华大学数学系）
题目：平均曲率流的进展
摘要：Some progresses on mean curvature flow are introduced.
（10）张希（中国科技大学数学科学学院）
题目：非线性偏微分方程和复几何中的典则度量
摘要：我们首先回顾复 Monge-Ampere 方程和 Hermitian-Einstein 方程的发展历史及研究现状，然后介绍近期我们关于复Monge-Ampere 方程正则性估计、褪化复 Monge-Ampere 方程弱解存在性及其应用、横截复 Monge-Ampere 方程和Sasakian-Einstein 度量存在性问题、全纯丛上渐近 Hermitian-Einstein结构存在性问题等方面的研究结果。

通俗报告人
（1）文兰（北京大学数学学院）
题目：康托定理和理发师悖论
摘要：
（2）罗懋康（四川大学数学学院）
题目：后面就是秘密-密码漫谈
摘要：
（3）张纪峰（中国科学院数学与系统科学研究院）
题目：我心中的控制论
摘要：控制论是集认识世界与改造世界与一体的交叉学科，涉及到工业、农业、交通、军事、资源、环境、经济、社会等领域中的许多复杂系统的建模、分析与调控。

自从1948 年诺伯特·维纳发表了著名的《控制论——关于在动物和机器中控制和通讯的科学》一书以来，控制论的思想和方法已经渗透到了许多自然科学和社会科学领域，其各阶段的理论发展及技术进步都与生产和社会实际需求密切相关。

该报告将利用报告人自己所熟悉的国内外控制论界的部分人物、事件和成果等，向大家展示一下控制论的伟绩和精彩，使大家对控制论的概念、研究对象、研究方向，及其意义有所了解。

希望吸引一批优秀的有志青年加入到控制论的研究队伍中来！
（4）田刚（北京大学数学学院）
题目：数学有用
摘要：
（5）崔俊芝（中国科学院数学与系统科学研究院）
题目：从科学计算到数字工程——谈谈相关的数学交叉科学研究
摘要：
（6）张立群（中国科学院数学与系统科学研究院）
题目：分析，长袖善舞
摘要：
（7）王师宬（北京大学数学科学学院）
题目：从打结谈起（陕西师范大学科普报告）
摘要：
（8）段海豹（中国科学院数学与系统科学研究院）
Title: Schubert calculus and cohomology of Lie groups （陕西师大）
Abstract: The problem of determining the cohomology ring of a Lie group was initiated by E. Cartan in 1929, and has been one of the main focuses of algebraic topology. On the other hand, Schubert calculus begun with the intersection theory of 19th century, and inspired by Hilbert's fifteenth problem, clarifying this calculus has been a major theme of 20 century algebraic geometry.
In this talk I shall explain the interaction between these two topics both with distinguished historical backgrounds, and demonstrate how the solution to the fundamental problem of Schubert calculus could lead to an explicit and unified construction for the integral cohomology ring of all 1-connected Lie groups.
（9）石钟慈（中国科学院数学与系统科学研究院）
题目：中国计算数学的发展
摘要：
（10）崔恒建（首都师范大学数学系）
题目:从女士品茶说起
摘要:这是一场故事汇，从上世纪二十年代“女士品茶”这一真实故事开始，由此爆料一系列发人深省的故事，一些如雷贯耳的大家名人将亮相。

这些真实故事的讲述，使人们在轻松和互动中得到启迪与感悟，领略到大自然和数据的奥秘，点亮你智慧人生。

体验到成功的背后是艰辛与坚持，原创的背后是探索与智慧。