Advanced Computational Electromagnetism -- ACE '06 Workshop

二十多年前开始的计算电磁学中的惠特尼形式革命，建立在离散霍奇理论的数学基础上，解决了雷-辛格猜想，并为丹尼斯·沙利文的理性同伦理论奠定了基础。基本工具指向Ed Witten的琼斯多项式TQFT方法的离散框架，以及相关的计算复杂性问题。此外，电气工程师和几何拓扑学家之间的这种互动在很大程度上被应用数学家所忽视！ACE '06将汇集非常不同领域的专家，继续从看似纯数学的技术转移到扩大计算电磁学范围所遇到的深层问题。电气工程师总是惊叹于麦克斯韦的电磁学理论和相关的数学形式主义之美。他们既思考了这幅大图景的实际含义，也思考了将其融入本科课程的困难。过去二十年的惠特尼形式革命将与马维尔方程相关的形式主义转化为离散设置，解决了计算电磁学中一些最深奥的问题，导致了非常高效的软件实现，使不可预见的应用得以解决，并为数学家提供了开放的研究问题。组织这次研讨会的一个主要目的是让多年前就被工程师引用过的关键数学家最终与工程界的关键人物接触！通过多样化的演讲、海报会议和小组讨论，ACE '06将通过带来来自不同国家、不同学科的专家、学生、教授和成功企业的工程师，保持强大的交叉施肥水平。更多信息可访问会议网页：http://www.bu.edu/eng/ace2006/

The Whitney form revolution in computational electromagnetics, initiated over two decades ago, builds on the mathematics which created discrete Hodge theory, solved the Ray-Singer conjecture and set the stage for Dennis Sullivan's approach to rational homotopy theory. The basic tools point to a discrete framework for Ed Witten's TQFT approach to the Jones polynomial, and associated computational complexity issues. Furthermore, this interaction between electrical engineers and geometrically minded topologists was largely unnoticed by applied mathematicians! ACE '06 will bring together experts in very diverse fields to continue this technology transfer from seemingly pure mathematics to deep problems encountered in enlarging the scope of computational electromagnetics.Electrical engineers have always marveled at the beauty of Maxwell's theory of electromagnetism and associated mathematical formalism. They have pondered both the practical implications of this big picture, and the difficulties of fitting it into the undergraduate curriculum. The Whitney form revolution of the past two decades has translated the formalism associated with Mawell's equations into a discrete setting, has resolved some of the deepest problems in computational electromagnetics, has lead to very efficient software implementations, has enabled unforeseen applications to be tackled, and has offered open research questions back to mathematicians. A major objective in organizing this workshop is to get key mathematicians who have been cited by engineers years ago, to finally rub shoulders with the key players within the engineering community! By having a diverse set talks, poster sessions, and panel discussions, ACE '06 will sustain the strong level of cross-fertilization by bringing from different countries, a diverse set of experts and academic disciplines, students, professors, and engineers who have grown successful companies. More information can be found on the conference webpage:http://www.bu.edu/eng/ace2006/