Algebra and Topology in Interaction; Davis, CA; September 2009

在由Yakov Eliashberg(斯坦福大学)、Nicolai Reshetikhin(加州大学伯克利分校)和Serge Tabachnikov(宾夕法尼亚州立大学)担任委员会主席的科学咨询委员会的指导下，PI和共同PI提议组织一次会议，名为相互作用中的代数和拓扑学，庆祝自Gelfand-Fuchs上同调诞生以来这两个领域相互作用的40年来的壮观发展。会议将于2009年9月在加州大学戴维斯分校校园举行。会议的主要主题是阐明过去40年来代数和拓扑学发展的特殊类型的相互作用，包括当代数学的最新成果。会议将讨论的主题包括当前辛场论、无限维李代数的表示和拓扑量子场论的令人兴奋的发展，以及在无限维李代数的上同调、特征叶类、接触同调、Chekanov-Eliashberg微分分次代数和Legendrian纽结理论的拓扑应用方面的最新成果。会议最重要的目标是为不同的数学家群体提供一个机会，包括博士后研究人员、那些传统上代表性较低的背景的人、研究生和来自小学本科院校的教师，与受邀的该领域的领先专家会面并讨论数学。为了促进讨论，主办方将尽一切努力将不同的听众带到会议上，并要求演讲者准备他们的演讲，目标是达到二年级研究生能够理解的水平。会议将把三代研究人员聚集在一起，促进一代之间的科学互动，为与会者之间交流思想和发起新的合作提供机会。年轻一代可以从领先的专家那里了解到专门针对他们的新确立的结果、新的观点和未来可能的研究方向。这些理论的创始人将介绍他们的发现是如何取得的，以及他们当时的愿景是什么。说明性演讲可以将这一愿景与当前的发展联系起来，给听众提供一种强烈的数学潮流和流动的感觉。与会者将专门用一次会议来汇编该领域中最有可能在不久的将来影响研究的未决问题的清单。会议还将包括传播成果的组成部分，以及向当地高中生和普通公众进行宣传。科学咨询委员会将为即将出版的会议论文集成立一个编辑委员会。为了体现会议的基调，将鼓励作者提供可供研究生阅读的说明性文章、调查论文和研究论文。在会议上介绍的会谈将由当地组织者放在会议网站上。外联活动将包括一位杰出发言者在会议期间的晚间会议上所作的介绍性发言。是次讲座是加州大学戴维斯分校数学系为期一年的外展活动的一部分，吸引了多达400名本地高中生和市民参加。

Under the guidance of the Scientific Advisory Board consisting of Yakov Eliashberg (Stanford University), Nicolai Reshetikhin (UC Berkeley), and Serge Tabachnikov (Pennsylvania State University) serving as Chair of the Board, the PI and Co-PIs propose to organize a conference, Algebra and Topology in Interaction, celebrating the 40 years of spectacular developments in the interplay of these two fields since the birth of the Gelfand-Fuchs cohomology. The conference will be held on the UC Davis campus in September 2009. The main theme of the conference is to illuminate the particular type of interaction which characterizes the past 40 years of developments in algebra and topology, including the most recent results in contemporary mathematics. The topics to be discussed in the conference will include the current exciting developments in symplectic field theory, representations of infinite- dimensional Lie algebras, and topological quantum field theory, as well as the recent achievements in the topological applications of cohomology of infinite-dimensional Lie algebras, characteristic classes of foliations, contact homology, Chekanov- Eliashberg differential graded algebra, and Legendrian knot theory. The most important goal of the conference is to provide an opportunity for a diverse group of mathematicians including postdoctoral researchers, those with traditionally underrepresented background, graduate students, and faculty from primary undergraduate institutions, to meet and discuss mathematics with the invited leading experts of the field. To facilitate the discussions, the organizers will make every effort to bring the diverse audience to the conference, and request the speakers to prepare their talks aimed at the level at which a second-year graduate student can understand.The conference will bring three generations of researchers together, and foster scientific interactions across the generation, providing an opportunity to exchange ideas and to initiate new collaborations among participants. The younger generation can learn the newly established results, new perspectives, and possible future directions of research specifically addressed to them from the leading experts. The founders of the theories will inject how their discoveries were made and what was their vision back then. Expository talks can connect this vision with the current developments, and provide to the audience a sense of strong current and flow of mathematics. The participants will devote one session to compiling a list of open problems in the area that are most likely to shape the research in the near future. The conference will also include components for dissemination of results as well as outreach to local high school students and the general public. The Scientific Advisory Board will form an editorial board for the conference proceedings volume to be published. Reflecting the tone of the conference, the authors will be encouraged to provide expository articles, survey papers, and research papers readable to graduate students. The talks presented at the conference will be placed on the Conference Website by the local organizers. The outreach activity will comprise an expository talk by a distinguished speaker in an evening session during the conference. This talk will be an integrated component of the year-long outreach activity of the Department of Mathematics, UC Davis, which brings as many as 400 local high school students and general public to the event.