申博sunbet官网现代数学研讨会

Wuhan Symposium on Modern Mathematics

June 4—7，2019 (Arrival: June 4)

Wuhan, China

数学中心和会场都在东校区创新研究院。

创新研究院与启明学院共一个大门（Entrance）。

在正式会议之前，6月4日下午举行“概率论，统计学与数据科学论坛----庆贺周元燊教授数学生涯终身成就”。

在正式会议之后，6月7日上午举行“随机分析与随机动力系统论坛

----庆贺黄志远教授数学生涯终身成就”。

Program

2019年6月4日
上午	报到
下午2pm-6pm 创新研究院（恩明楼）205室	概率论，统计学与数据科学论坛 ----庆贺周元燊教授数学生涯终身成就 Celebrating Professor Yuan-Shih Chow’s Lifetime Achievement 组织者：李照海
主持人：李照海	浙江大学贺词 2:00-2:05 黎子良与周良蒂祝词 2:05-2:10
	报告人：熊昭2:10-2:35
	报告人：张存惠2:40-3:05
主持人：张虎	报告人：应志良3:10-3:35
	报告人：刘爱义3:40-4:05
茶歇4:05-4:20
主持人：刘继成，刘妍岩	报告人：林正炎4:20-4:45
	报告人：David Siegmund &方笑 4:50-5:15
	报告人：张朋5:20-5:45

6月5日数学中心现代数学研讨会
上午8:30am 创新研究院（恩明楼）一楼大会议厅	开幕式
上午9am—12noon 创新研究院（恩明楼）一楼大会议厅
主持人：方复全	报告人：王跃飞9:00-9:25
	报告人：曹进德9:30-9:55
	报告人：刘小博10:00-10:25
茶歇10:30-10:45
主持人：白承铭	报告人：陈大岳10:45-11:10
	报告人：陈猛11:15-11:40
	报告人：吴泉水11:40-12:05
下午2pm-6pm 创新研究院（恩明楼）205室
主持人：李佳	报告人：严树森（李国平数理科学讲座）2:00-2:25
主持人：刘斌，王湘君	报告人：谈胜利2:30-2:55
	报告人：秦厚荣3:00-3:25
	报告人：林亚南3:30-3:55
茶歇4:00-4:15
主持人：吴军，吴付科	报告人：范辉军4:15-4:40
	报告人：谢资清4:45-5:10
主持人：张雄韬	报告人：李用声5:15-5:40
	报告人：陈建兵5:45-6:10
下午6:30pm	乘车访问华中师范大学

6月6日数学中心现代数学研讨会
上午9am—12noon 创新研究院（恩明楼）205室
主持人：赵会江，殷钶	报告人：黄飞敏9:00-9:25
	报告人：章梅荣9:30-9:55
主持人：林聪萍	报告人：许学军10:00-10:25
	茶歇10:30-10:45
主持人：陈家清	报告人：汤华中10:45-11:10
	报告人：黄建华11:15-11:40
下午2pm-6pm 创新研究院（恩明楼）205室
主持人：周焕松，张一威	报告人：王亚光2:00-2:25
主持人：彭双阶，刘凯	报告人：邵井海2:30-2:55
	报告人：向淑晃3:00-3:25
茶歇3:30-3:45
主持人：王维真，徐海涛	报告人：许勇3:50-4:15
	报告人：雍稳安4:20-4:45

6月7日
上午9am—11noon 创新研究院（恩明楼）813室	随机分析与随机动力系统论坛 ---庆贺黄志远教授数学生涯终身成就 组织者：段金桥，王湘君，李楚进
主持人：王湘君	武汉大学贺词9:00-9:10
	报告人：骆顺龙9:10-10:00
	报告人：王才士10：05-11:00

会议地点:

6月5日上午开幕式在申博sunbet官网创新研究院（恩明楼）一楼会议厅。6月4日下午，6月5日下午，6月6日全天报告均在创新研究院（恩明楼）205室。 6月7日报告在创新研究院（恩明楼）813室。

住宿 ：

地点：申博sunbet官网国际学术交流中心8号楼(从南二门或东北门进园。请参见校园地图)

湖北 武汉洪山区珞喻路1037号

电话：027-8754 0188

如何去数学中心和会场(都在东校区创新研究院)：

Bus 接送。创新研究院与启明学院共一个大门（Entrance）。

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Abstracts

6月4日

Speaker: Chao A. Hsiung

Title: Smoothed Lexis Diagrams with Applications to Cancer Surveillance

Abstract: Smoothed Lexis diagram was constructed by using Poisson model together with Bayesian priors through the coefficients of Bernstein polynomials. This method was applied to study the effects of age, period and cohort on incidence rates of cancers. Real data examples will demonstrate its use in public health problems.

( joint works with Prof. I-Shou Chang, Dr. Li-Chu Chien and Dr. Li-Hsin Chien)

Speaker: Cun-Hui Zhang（Rutgers University, New Brunswick, USA）

Title: Exchangeability, Multivariate Nonlinear Correlation,Gaussian Copulas, and Additive Regression

Abstract: The maximum correlation of functions of a pair of random variables is an important measure of stochastic dependence. It is known that this maximum nonlinear correlation is identical to the absolute value of the Pearson correlation for a pair of Gaussian random variables or a pair of nested sums of iid random variables. This paper extends these results to multiple sums of subsets from a collection of exchangeable random variables and pairwise Gaussian processes and vectors. Applications to additive regression and Gaussian copulas will be discussed. This is joint work with Zijian Guo.

Speaker: Zhiliang Ying

Title: Some new results on sequential likelihood ratio test

Speaker: Aiyi Liu

Title: Nonparametric Estimation of Distributions and Diagnostic Accuracy Based on

Group-Tested Results with Differential Misclassification

Abstract: This article concerns the problem of estimating a continuous distribution in a diseased or non-diseased population when only group-based test results on the disease status are available.   The problem is challenging in that individual disease statuses are not observed and testing results are often subject to misclassification, with further complication that the misclassification may be differential as the group size and the number of the diseased individuals in the group vary. We propose a method to construct nonparametric estimation of the distribution and obtain its asymptotic properties. The performance of the distribution estimator is evaluated under various design considerations concerning group sizes and classification errors.  The method is exemplified with data from the National Health and Nutrition Examination Survey (NHANES) study to estimate the distribution and diagnostic accuracy of blood monocyte percent in serum samples in predicting chlamydia incidence.

Speaker: 林正炎

Title: On weak convergence of stochastic processes

Abstract: From the classical theory of weak convergence of probability measures, we introduce the Donsker theorem in the talk.The emphasis is on the introduction of modern theory. Weak convergence of various general functionals of partial sums of dependent random variables (statistics) to stochastic integrals now plays an important role in the modern probability theory and statistical theory. We introduce the weak convergence of various general functionals of partial sums of causal processes to stochastic integrals driven by Brownian motion and various general functionals of partial sum processes of i.i.d. random variables with heavy tail to stochastic integrals driven by Levy stable processes.

Speaker: Xiao Fang

Title: Segmentation and Estimation of Change-point Models: False Positive Control and Confidence Regions

Abstract: To segment a sequence of independent random variables at an unknown number of change-points, we introduce new procedures that are based on thresholding the likelihood ratio statistic, and give approximations for the probability of a false positive error when there are no change-points. We also study confidence regions based on the likelihood ratio statistic for the change-points and joint confidence regions for the change-points and the parameter values. Applications to segment array CGH data are discussed. This is joint work with Jian Li and David Siegmund.

Speaker: Peng Zhang

Title: Clustering sparse categorical data with mixture models.

6月5日

题目： On dynamics of entire maps with symmetry

报告人： 王跃飞

摘要：We will talk about recent results on the dynamics of holomorphic maps with certain symmetries, including families of Baker’s wandering maps, exponential maps and hyperbolic maps, cosine maps etc. Such a map either contains a dynamical ray in its Julia set or has a wandering domain. Moreover, any connected compact set containing the point on the ray and its forward image point intersects its Julia set.

题目： 网络群智协同与控制

报告人： 曹进德（东南大学）

摘要：本报告涵盖群智网络的研究背景及应用，网络群智协同与优化， 网络牵制控制等。

题目： 射影代数簇的典范分类现状

报告人： 陈猛（复旦大学）

摘要：本报告主要介绍射影代数簇的典范线性系统所诱导的双有理几何分类的思想和研究现状。

题目： Skew Calabi-Yau algebras, Homological Determinants and Nakayama Automorphisms

报告人： 吴泉水

摘要：Noncommutative Calabi-Yau algebras is an analogue of the coordinate ring of Calabi-Yau variety in noncommutative algebraic geometry. Artin-Schelter regular algebras and lots of quantum groups are examples of skew Calabi-Yau algebras. A skew Calabi-Yau algebra is Calabi-Yau algebra if and only if its Nakayama automorphism is inner. Homological determinants of quantum actions on skew Calabi-Yau algebras will be defined, which can be viewed as a generalization of the usual determinants (of graded automorphism of polynomial algebras). Some applications will also be given at the end of the talk.

题目：Non-degeneracy of multi-bubbling solutions

报告人：严树森

摘要：We consider the prescribed scalar curvature equations. Using the Pohozaev identities, we first prove a non-degeneracy result for the positive multi-bubbling solutions constructed by Wei and Yan.We then use this non-degeneracy result to glue together bubbles with different concentration rate to obtain new solutions.

题目：Connecting Hodge integrals to Gromov-Witten invariants by Virasoro operators

报告人：刘小博

摘要：Kontsevich-Witten tau function and Hodge tau functions are important tau functions for KP hierarchy which arise in geometry of moduli space of curves. Alexandrov conjectured that these two functions can be connected by Virasoro operators. In a joint work with Gehao Wang, we have proved Alexandrov's conjecture. In a joint work with Haijiang Yu, we show that this conjecture can also be generalized to Gromov-Witten invariants and Hodge integrals over moduli spaces of stable maps to smooth projective varieties.

  题目：代数几何与智能数学
  报告人：谈胜利 （华东师范大学）
  摘要：本演讲试图探讨代数几何在新时代的新应用，介绍近年来代数几何中的 Hodge 分解理论在博弈论中的初步应用，代数几
何的不变量和分类的思想可能的新应用。

题目：On gauged linear sigma model

报告人：范辉军（北京大学）

摘要：Gauged linear sigma model was a physical model proposed by E. Witten in the early of 90's, which was used by him to explain the mirror symmetry phenomenon. Only up to recent years has this model been seriously considered by mathematicians with the development of Gromov-Witten theory and quantum singularity theory (FJRW theory). In this talk, I will report our progress on this topic.

题目：Solving Singularly Perturbed Neumann Problems for Multiple Solutions

报告人：谢资清

摘要：In this talk, based on the analysis of bifurcation points and Morse indices of trivial solutions at any perturbation value, the generating process of nontrivial positive solutions for a general singularly perturbed Neumann boundary value problem is developed. The bifurcation points of each trivial solution and then the exact critical perturbation value $\varepsilon_c$ which determines the existence or non-existence of nontrivial positive solutions are verified. An efficient local minimax method based on the bifurcation and Morse theory is proposed to compute both M-type and W-type saddle points by introducing an adaptive local refinement strategy, a continuation strategy for initial selection and the Newton method to improve the convergence speed.  Extensive numerical results are reported to investigate the critical value $\varepsilon_c$ and present interesting properties of different types of multiple solutions.

题目：Admisissible homomorphism and coherent sheaves over weighted projective lines of tubular type 

报告人：林亚南（厦门大学）

摘要：We classify all the coherent sheaves categories over the weighted
projective lines of tubular type and of domestic type in the sense of admissible homomorphisms, and show that how to relate the weighted projective lines of wild type via equivariantization by using admissible homomorphisms. This is joint work with Jianmin Chen, Shiquan Ruan and Hongxia Zhang.

题目：同余数问题与K_2

报告人：秦厚荣

摘要： 同余数问题有着悠久的历史，研究结果丰富. 最近我们给出了同余数的一个新判别法则.利用这个判别法则，我们可以简化很多已有结果的证明，同时也在模8 余1,2,3的情形给出系列新结果。特别地，我们将建立Milnor群与同余数之间的联系。根据得到的结果，我们将提出相关猜想。

题目：Global large solutions to the 3D compressible Navier-Stokes equations

报告人：李用声（华南理工大学）

摘要：In this talk we discuss the 3-D compressible Navier-Stokes equations. We show the existence of the global large solutions in the critical Besov spaces with initial data satisfying a nonlinear smallness condition. Here the “large solutions” mean that the any component of the initial velocity could be arbitrarily large. Moreover, we give an example of initial data satisfying the nonlinear smallness condition, while the norms of each component are arbitrarily large.

题目：Uncertainty Quantification and Propagation in Nonlinear Systems: Advances and Mathematical Challenges

报告人：陈建兵（同济大学）

摘要： To quantify uncertainties in engineering accurately and efficiently is essential to the safety of civil engineering. Engineering structures usually exhibit strong nonlinear behaviors, and simultaneously, there are large degree of randomness in both structural properties and disastrous dynamic excitations, e.g., earthquakes and strong wind, etc. Such coupling of nonlinearity and randomness leads to great challenges in the analysis of real-world structures. To this end, in the past over 10 years, we developed a family of probability density evolution method (PDEM), where the principle of preservation of probability is advocated as a basis of stochastic dynamics, and the physical mechanism/physical equations are incorporated into the random event description of this principle, leading to the generalized density evolution equation. In contrast to the traditional equations (e.g., FPK equation), the governing equation is a one-dimensional equation and therefore can be applied to complex systems. Error estimate of the numerical algorithm based on the extended Koksma-Hlawka inequality was established, yielding a GF-discrepancy minimized optimal point selection strategy. In addition, combined with the change of probability measure and Radon-Nikodym derivative, a probabilistically logic consistent framework for the quantification of simultaneous aleatory and epistemic uncertainties was established. This provides a possible tool for real-time reliability evaluation/updating of complex structures/systems based on the data from health monitoring systems. Some engineering applications are illustrated. Existing mathematical challenges are discussed.

6月6日

报告人：章梅荣（清华大学）

题目：线性与非线性薛定谔方程之间的联系与问题

摘要：Lagrange的分析力学是从能量的观点来建立静动态方程，而量子力学中的能量表现为特征值。在本报告中，我们将从常微分方程的特征值对于位势的完全连续性出发，建立静态的线性和非线性薛定谔方程（组）的一些内在联系，并导出一系列的非线性常微分方程组。这些方程（组）的完全可积性和极限方程等等是值得研究并有待研究的问题。

报告人：许学军（同济大学 数学科学学院，中科院数学与系统科学研究院）

题目：Local Multigrid with Applications

摘要：In this talk, we shall present a local multigrid algorithm for solving the linear algebraic systems arising from the adaptive continuous and discontinuous finite element methods. The abstract Schwarz theory is applied to analyze the multigrid method with Jacobi or Gauss-Seidel smoother performed on local nodes on each level. It is shown that the local multigrid method is optimal, which means that the convergence rate is independent of the mesh size and mesh level.

报告人：汤华中

题目：Physical-constraints-preserving schemes for special relativistic magnetohydrodynamic equations

摘要：We first study the admissible state set G of special relativistic magnetohydrodynamics (RMHD). It paves a way for developing physical-constraints-preserving (PCP) schemes for the special RMHD equations with the solutions in G. To overcome the difficulties arising from the extremely strong nonlinearities and no explicit formulas of the primitive variables and the flux vectors with respect to the conservative vector, two equivalent forms of G with explicit constraints on the conservative vector are skillfully discovered. The first is derived by analyzing roots of several polynomials and transferring successively them, and further used to prove the convexity of G with the aid of semi-positive definiteness of the second fundamental form of a hypersurface. While the second is derived based on the convexity, and then used to show the orthogonal invariance of G. The LxF splitting property does not hold generally for the nonzero magnetic field, but by a constructive inequality and pivotal techniques, we discover the generalized LxF splitting properties, combining the convex combination of some LxF splitting terms with a discrete divergence-free condition of the magnetic field. Based on the above analyses, several 1D and 2D PCP schemes are then studied. In the 1D case, a first-order accurate LxF-type scheme is first proved to be PCP under the CFL condition, and then the high-order accurate PCP schemes are proposed via a PCP limiter. In the 2D case, the discrete divergence-free condition and PCP property are analyzed for a first-order accurate LxF-type scheme, and two sufficient conditions are derived for high-order accurate PCP schemes. Our analysis reveals in theory for the first time that the discrete divergence-free condition is closely connected with the PCP property. Several numerical examples demonstrate the theoretical findings and the performance of numerical schemes.

报告人：王亚光

题目：Back flow of the Prandtl boundary layer

摘要：In this talk, we study the back flow point of the Prandtl boundary layer under an adverse pressure gradient. The occurrence of back flow is an important physical event in the evolution of boundary layer, which eventually leads to separation. For the two-dimensional unsteady Prandtl boundary layer equations, we obtain the existence of a back flow point on the boundary when the initial tangential velocity is strictly monotonic with respect to the normal variable, and the pressure gradient of the outer flow is adverse.

报告人：黄建华

题目：随机带阻尼的2n+1阶KDV方程不变测度及其多项式混合性.

摘要：我们建立带阻尼的2n+1阶随机KDV方程的局部适定性和整体适定性, 证明其马氏半群存在唯一的不变测度,并且不变测度是遍历的，由于其弱耗散性，我们利用Foias-Prodi估计方法给出其是多项式混合的。

报告人：邵井海

题目：The existence of optimal control for continuous-time Markov decision processes in random environments

摘要：In this talk, we investigate the optimal control problem for continuous-time Markov decision processes with the random impact of the environment. We provide conditions to show the existence of optimal controls under finite-horizon criteria. Under appropriate conditions, the value function is continuous and satisfies the dynamic programming principle. These results are established by introducing some restriction on the regularity of the optimal controls and by developing a new compactification method for continuous-time Markov decision processes, which is originally used to solve the optimal control problem for jump-diffusion processes.  This is a joint work with Kun Zhao.

报告人：向淑晃

题目：Interpolation and Expansion on Orthogonal Polynomials

摘要：The convergence rates on polynomial interpolation in most cases are estimated by Lebesgue constants. These estimates may be overestimated for some special points of sets for functions of limited regularities. In this talk, new formulas on the convergence rates are considered. Moreover, new and optimal asymptotics on

the coecients of functions of limited regularity expanded in forms of Jacobi and Gegenbauer polynomial series are presented. All of these asymptotic analysis are optimal. Numerical examples illustrate the perfect coincidence with the estimates.

报告人：许勇, 裴斌

题目：Stochastic averaging for stochastic differential equationsdriven by a Wiener process and fractional Brownian motion

摘要：We focus on stochastic differential equations involving both a Brownian motion and fractional Brownian motion. The integral w.r.t. Brownian motion is the standard Itô integral, and the integral w.r.t. fBm is pathwise generalized Lebesgue–Stieltjes integral. An averaged SDE for the original SDE is proposed, and their solutions are quantitatively compared. It is shown that the solution of the averaged SDE converges to that of the original SDE in the sense of mean square and also in probability. This averaging principle paves a way for reduction of computational complexity. The implication is that one can ignore the complex original systems and concentrate on the average systems instead.

6月7日

报告人：骆顺龙

题目：Asymmetry versus Coherence

摘要：By exploiting the algebraic and geometric structure of operation-state coupling, we show that an information-theoretic measure of asymmetry emerges naturally from the formalism of quantum mechanics. This is achieved by decomposing the operation-state coupling into a symmetric part and an asymmetric part, which satisfy a conservation relation. The symmetric part is represented by the symmetric Jordan product, and the asymmetric part is synthesized by the skew-symmetric Lie product. The latter leads to a significant extension of the celebrated Wigner-Yanase skew information, and has an operational interpretation as quantum coherence of a state with respect to an operation. This presents a basic framework for quantitatively addressing symmetry-asymmetry complementarity.

报告人：王才士

题目：Spectral Results Concerning Quantum Bernoulli Noises and Application

摘要：Quantum Bernoulli noises are creation and annihilation operators acting on Bernoulli functionals. In this talk, we would like to show some spectral results concerning quantum Bernoulli noises and their application to quantum random walks.

Center for Mathematical Sciences

Huazhong University of Science and Technology, Wuhan, China

mathcenter.hust.edu.cn

      Center for Mathematical Sciences, at Huazhong University of Science and Technology, Wuhan, China, is a mathematical research and education institution. Its mission is to promote interactions between mathematics and other disciplines, and to connect branches of mathematics. The Center fulfills its mission by conducting select research and educational activities, including short courses, workshops, mini-workshops, and topic conferences.

申博sunbet官网数学中心

mathcenter.hust.edu.cn

数学作为一门基础学科，一直在背后推动着科学和工程技术的进步，为现代科学和高新技术的发展奠定基础。通讯与网络安全，金融市场与风险，国防和国家安全，无不与数学紧密相关。科学技术史和当代科技发展趋势明确无误地告诉我们：科技强国必定是数学强国，而现代高科技竞争同时包含数学研究的竞争。本中心宗旨：一方面积极倡导数学不同分支之间的相互交叉研究，激发新的合作研究，并催生新的研究领域和研究群体。另一方面，努力推动数学与科学、工程、医学、经济与金融学之间的相互交叉研究，引导数学家和科学家之间建立起广泛的联系，从对方的研究活动中吸取养分和获取动力，从而达到合作共赢。本中心和sunbet中国官网并其它院系，兄弟院校以及科研机构紧密合作，促进数学、应用数学与统计学的发展。在这个过程中，努力培养和吸引优秀人才，服务国家和社会。