International Conference on Sequences and Codes

该项目支持来自美国大学的早期职业数学家参加关于序列和编码的国际会议。它由奈杰尔·波士顿(威斯康星州)、罗伯特·卡尔德班克(普林斯顿)和乔纳森·杰德瓦布(西蒙·弗雷泽大学)组织，将于2006年7月17日至21日在加拿大温哥华举行。更多信息可在http://www.pims.math.ca/science/2006/06seqcodesThis会议的网络上获得，这将有助于发展一支拥有强大计算和分析工具的数学科学家核心，他们对在跨学科背景下应用数学感到兴奋。应用影响的一个例子是诸如Clifford代数之类的代数和组合结构对多天线无线通信系统的跨层设计的价值。参与数学科学界的价值在于在不超过单天线系统的信号处理复杂性的情况下实现多天线系统的前景。另一个例子来自新兴的多天线雷达领域，在该领域，波形的设计和随后的回波处理决定了雷达区分目标和杂波、区分近距离目标和在复杂场景中检测小目标的能力。所有这些都是关键的操作问题。会议将增加早期职业数学家的人才库，他们认识到数学的力量及其在工程学科中所起的重要作用。它将促进跨学科的探索和广度，并帮助早期职业数学家在与不同学科相关的不同文化中蓬勃发展。这种连接不同世界的能力对学术和非学术职业的成功越来越重要。重点是理论和应用之间的协同，因为信息理论和编码是通过发现新的应用而进步的学科。会议将展示最近出现这种协同效应的例子，特别是用于无线通信的空时码和Clifford代数、量子信息理论和量子纠错码、雷达和序列设计。不断发展的应用程序环境有助于定义新的理论领域，并为什么被认为是有趣的东西提供衡量标准。以具体例子为基础的基本理论的发展往往说明了正确的抽象，随着理论和实践的共同发展，这种抽象成为新的原语。当这种协同作用不存在时，总是存在理论脱离其原始应用背景并失去相关性的风险。

This project supports participation by early career mathematicians from US universities in an International Conference on Sequences and Codes. It is organized by Nigel Boston (Wisconsin), Robert Calderbank (Princeton) and Jonathan Jedwab (Simon Fraser University), and will take place July 17-21, 2006 in Vancouver, Canada. More information is available on the web at http://www.pims.math.ca/science/2006/06seqcodesThis conference will contribute to the development of a core of mathematical scientists armed with powerful computational and analytical tools who are excited about applying mathematics in an interdisciplinary context. One example of applications impact is the value of algebraic and combinatorial structures such as Clifford algebras to cross layer design of multiple antenna wireless communication systems. The value of engaging the mathematical sciences community is to realize the promise of multiple antenna systems without exceeding the signal processing complexity of single antenna systems. Another example comes from the emerging area of multiple antenna radar, where thedesign of the waveform and the subsequent processing of the return determine the ability of the radar to discriminate targets from clutter, to discriminate closely spaced targets, and to detect small targets in complex scenes. All these are critical operational issues.The conference will increase the pool of early career mathematicians who appreciate the power of mathematics and the important role that it plays in engineering disciplines. It will promote interdisciplinary exploration and breadth, and help early career mathematicians flourish in the different cultures associated with the different academic disciplines. This ability to bridge different worlds is a quality that is increasingly important to success in both academic and non-academic careers.The emphasis is on the synergy between theory and application, since information theory and coding are subjects that advance by discovering new applications. The conference will feature recent examples where this synergy is present, specifically space-time codes for wireless communication and Clifford algebras, quantum information theory and quantum error correcting codes, radar and sequence design. The evolving applications context helps to define new areas of theory and provides measures for what is considered interesting. The development of a fundamental theory grounded in specific examples often illuminates the right abstraction, one that becomes a new primitive as theory and practice evolve together. When this synergy is not present there is always a risk that the theory will become detached from its original applications context and lose relevance.