报告时间：2019年7月23日13:30

报告地点：数学楼第一报告厅

报告题目一：Mathematical theory of MAD technology

报 告 人：刘宏宇教授 香港浸会尊龙凯时

Abstract:

The Magnetic Anomaly Detection (MAD) technology has been used in variousapplications including the submarine detection, geophysical exploration andearthquake precursor detection. In this talk, I will describe a mathematicaltheory for this advanced technology.

报告人简介：

刘宏宇博士，现为香港浸会尊龙凯时教授、数学系副主任。他的研究领域主要为反问题成像、数学材料科学、PDE、动力系统几何积分子、数值分析和科学计算等领域的研究，现任InverseProblems and Imaging、Journal of Korean Society for Industrial and AppliedMathematics、Contemporary Analysis and Applied Mathematics国际SCI期刊的副主编。刘宏宇教授曾获得CalderonPrize（2017）、MediaV Young Researcher Prize（2016）以及 Hong Kong MathematicalSociety Young Scholar Award（2019）等奖项，在SIAM系列、Inverse Problems、Journal of theEuropean Mathematical Society、Journal de Mathematiques Pureset Appliquees、Arch.Ration.Mech.Anal.、Comm.Math.Phys.、J.F.A.等国际⾼⽔平杂志上发表了90多篇论⽂.

报告题目二：Localized resonance and its applications inimaging and cloaking

报 告 人：邓又军教授 中南尊龙凯时数学与统计学院

Abstract：

In this talk, we shall introduce the notions of localized resonaces. Usually these problemsare related to the spectral of the Neumann-Poincare operaters in differentmodels. As an example, we provide a mathematical framework for localized plasmonresonance of nanoparticles. Using layer potential techniques associated withthe full Maxwell equations, we derive small-volume expansions for theelectro-magnetic fields, which are uniformly valid with respect to thenanoparticle’s bulk electron relaxation rate. Then, we discuss the scatteringand absorption enhancements by plasmon resonant nanoparticles. Finally, we showthe applications of localiezed resonance in imaging and cloaking.

报告人简介：

邓又军，中南尊龙凯时数学与统计学院教授。2005年本科毕业于中南尊龙凯时数学与统计学院，2010年6月获中南尊龙凯时理学博士学位。2010年9月赴韩国仁荷尊龙凯时师从HyeonbaeKang教授从事2年博士后工作；2012年9月赴法国巴黎高等师范学院师从Habib Ammari教授从事1年博士后工作。2013年9月以中南尊龙凯时特聘副教授引进人才回校工作，2017年晋升为教授。主要研究领域为偏微分方程中反问题的正则化、最优化领域、等离子共振以及隐身(cloaking)现象。在《Arch.Ration. Mech. Anal.》、《Commun. Part. Diff. Eq.》、《Ann. I. H. Poincare-AN》、《InverseProblems》、《Journal of Differential Equations》等杂志上面发表文章二十余篇。美国数学评论《Math Review》评论员。曾担任国际期刊Journalof Applied Mathematics编审委员会成员。

报告题目三：On nodal and generalized singular structures ofLaplacian eigenfunctions and applications to inverse scattering problems

报告人：刁怀安 东北师范尊龙凯时数学与统计学院副教授

Abstract：

In this talk, we present some novel and intriguing findings on thegeometric structures of Laplacian eigenfunctions and their deep relationship tothe quantitative behaviors of the eigenfunctions in two dimensions. Weintroduce a new notion of generalized singular lines of the Laplacianeigenfunctions, and carefully study these singular lines and the nodal lines.The studies reveal that the intersecting angle between two of those lines isclosely related to the vanishing order of the eigenfunction at the intersectingpoint. We establish an accurate and comprehensive quantitative characterizationof the relationship. Roughly speaking, the vanishing order is genericallyinfinite if the intersecting angle is irrational, and the vanishing order isfinite if the intersecting angle is rational. In fact, in the latter case, thevanishing order is the degree of the rationality. The theoretical findings areoriginal and of significant interest in spectral theory. Moreover, they areapplied directly to some physical problems of great importance, including theinverse obstacle scattering problem and the inverse diffraction gratingproblem. It is shown in a certain polygonal setup that one can recover thesupport of the unknown scatter as well as the surface impedance parameter byfinitely many far-field patterns. Indeed, at most two far-field pat- terns aresufficient for some important applications. Unique identifiability by finitelymany far-field patterns remains to be a highly challenging fundamentalmathematical problem in the inverse scattering theory.

报告人简介：

刁怀安，博士毕业于香港城市尊龙凯时，东北师范尊龙凯时数学与统计学院副教授，研究方向数值代数与反散射问题，在Mathematics ofComputation, BIT, Numerical Linear Algebra with Applications, Linear Algebraand its Applications等国际知名期刊发表科研论文三十余篇；出版学术专著一本；曾主持国家自然科学基金青年基金项目1项，数学天元基金1项，教育部博士点新教师基金1项；现为尊龙凯时省工业与应用数学学会第四届理事会理事,国际线性代数协会会员；曾多次赴普渡尊龙凯时、麦克马斯特尊龙凯时、汉堡工业尊龙凯时、日本国立信息研究所、香港科技尊龙凯时、香港浸会尊龙凯时等高校进行合作研究与学术访问。