Strings and automorphic forms in algebraic topology

代数拓扑中的串和自守形式

• 批准号: 1228196
• 负责人: Matthew Ando
• 金额: $ 4.18万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-07-15 至 2013-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1228196&HistoricalAwards=false
• 关键词: Strings; automorphic; forms; algebraic; topology

AbstractAward: DMS 1228196, Principal Investigator: Matthew AndoThis project will support travel to the conference "Strings and automorphic forms in algebraic topology" at the University of Bochum in August 2012. The title refers to the intersection between string theory, number theory, and homotopy theory which began with the study of elliptic cohomology in the 1980s. In the last ten years the areas of significant progress have broadened considerably, involving many new research topics. For example, Behrens and Lawson have introduced generalizations of topological modular forms, using the Shimura varieties which play an important role in the Langlands conjecture. For another, the spectacular progress in higher category has led to a much better understanding of quantum field theory and the String 2-group, which are intimately but still mysteriously related to the geometry of elliptic cohomology. The conference will bring together researchers and graduate students working in these areas, to facilitate the sharing of results, the establishment of new collaborations, and the training of the next generation of researchers in this area. The roots of the fields which this conference brings together--String theory, number theory, and algebraic topology--are far apart, and their interaction via elliptic cohomology has, in the best tradition of interdisciplinary research, led to spectacular advances in algebraic topology in the last twenty-five years. One of the appealing features of the subject is that it consistently attracts excellent new researchers from different areas of mathematics and physics, and those new researchers bring exciting new points of view. In the last five years, some of the exciting emerging research teams are based in Europe. The conference will bring together current leaders and new researchers, enabling interaction and cross-fertilization of ideas among a broad group of mathematicians. The project will support travel and participation by US-based mathematicians, especially graduate students and recent PhDs, to help them become involved in this exciting area of research. The web site for the conference is http://www.ruhr-uni-bochum.de/ffm/Lehrstuehle/Lehrstuhl-XIII/conf12.html

AbstractAward：DMS 1228196，首席研究员：Matthew Ando该项目将支持前往波鸿大学参加2012年8月的“代数拓扑中的字符串和自守形式”会议。 标题是指弦理论，数论和同伦理论之间的交叉点，始于20世纪80年代的椭圆上同调研究。 在过去的十年中，取得重大进展的领域大大拓宽，涉及许多新的研究课题。 例如，贝伦斯和劳森利用在朗兰兹猜想中发挥重要作用的志村变种引入了拓扑模形式的推广。另一方面，在更高范畴上的惊人进展使人们对量子场论和弦2群有了更好的理解，它们与椭圆上同调几何有着密切但仍然神秘的联系。会议将汇集在这些领域工作的研究人员和研究生，以促进成果的共享，建立新的合作，并在这一领域的下一代研究人员的培训。 本次会议汇集的领域的根源-弦理论，数论和代数拓扑-相距甚远，它们通过椭圆上同调的相互作用，在跨学科研究的最佳传统中，导致了代数拓扑在过去二十五年中的巨大进步。 该主题的吸引力之一是它不断吸引来自数学和物理学不同领域的优秀新研究人员，这些新研究人员带来了令人兴奋的新观点。在过去的五年里，一些令人兴奋的新兴研究团队位于欧洲。 会议将汇集当前的领导者和新的研究人员，使一个广泛的数学家群体之间的互动和思想的交叉施肥。该项目将支持美国数学家的旅行和参与，特别是研究生和最近的博士生，以帮助他们参与这一令人兴奋的研究领域。 会议的网址是http://www.ruhr-uni-bochum.de/ffm/Lehrstuehle/Lehrstuhl-XIII/conf12.html