Conference: Motives, Quantum Field Theory and Pseudodifferential Operators

2008年6月2日至14日，波士顿大学将主办“动机、量子场论和伪微分算符”会议。这次会议将包括关于这些已建立的领域之间迅速发展的关系的入门和高级讲座。由于这些研究领域的基本工具有很大不同，会议不同方面的专家需要对其主题进行概述，并指出这些主题之间的相互作用。来自美国和欧洲的演讲者和参与者受到了邀请。来自三个会议领域的30多位顶尖数学家已经同意参加，包括斯宾塞·布洛赫、阿兰·康尼斯、亚历山大·贡查罗夫、德克·克里默和理查德·梅尔罗斯。这次会议预计将有大约75-100名数学家和数学物理学家参加。动机、量子场论和伪微分算符这三个领域作为独立的领域得到了很好的确立和活跃，但直到过去十年，它们一直被视为本质上互不相交的企业。动机理论是由Grothendieck在20世纪60年代发展起来的，它是一个融合了各种上同调理论的算术代数几何体系。微扰量子场理论最早出现在1945年左右，用来解释量子电动力学和其他场论中的实验室结果，并在很大程度上依赖于费曼积分的计算。最后，起源于20世纪60年代的伪微分算符理论是在一个集合中处理所有经典微分算符、格林算符和热算符的框架。直到最近，这些明显不同的领域之间的联系主要局限于量子场论中格林算符的出现。多个Zeta值出人意料地出现为Feynman积分值，这表明量子场论和动机之间存在着深刻的联系，这是多个Zeta函数的常见设置。此外，由Connes和Kreimer发现的编码Feynman积分的复杂组合的Hopf代数结构出现在多重Zeta值理论和伪微分算子的符号计算中。进一步的研究表明，这些联系不仅仅是巧合，Bloch，Connes，Esnault，Kreimer，Marcoli和其他人的工作指出了非对易几何解释或直接动机/量子场论联系的可能性。这是美国第一次关于这一主题的会议。由于初级教师和研究生被鼓励在NSF的部分支持下参加，日程安排将包括关于三个会议区域的介绍性讲座以及关于Hopf代数和多重Zeta函数的讲座。其他发言者将就会议领域进行研究级别的演讲，特别强调他们的互动。

On June 2-14, 2008, Boston University will host the conference Motives, Quantum Field Theory, and Pseudodifferential Operators. This conference will featureboth introductory and advanced lectures on the rapidly developing relationships among these established fields. Since the fundamental tools in these research areas are quite different, there is a need for experts in different aspects of the conference to both present overviews of their subjects and point out the interactions among these topics. Speakers and participants have been invited from the US and Europe. Already over 30 top mathematicians from the three conference fields have agreed to attend, including Spencer Bloch, Alain Connes, Alexander Goncharov, Dirk Kreimer, and Richard Melrose. The attendance for this conference is expected to be roughly 75 -- 100 mathematicians and mathematical physicists. The three fields of motives, quantum field theory, and pseudodifferential operators are well established and active as independent fields, but until the past decade they have been viewed as essentially disjoint enterprises. The theory of motives was developed by Grothendieck in the 1960s as an arithmetic algebraic geometric setup incorporating diverse cohomology theories. Perturbative quantum field theory first appeared around 1945 to explain laboratory results in quantum electrodynamics and other field theories, and depends heavily on the calculation of Feynman integrals. Finally, the theory of pseudodifferential operators, dating from the 1960s, is a framework to treat all classical differential, Green's and heat operators in one setting.Until recently, connections among these apparently very different fields were limited mainly to the appearance of Green's operators in quantum field theory. The unexpected appearance of multiple zeta values as values of Feynmanintegrals indicated a deep connection between quantum field theory and motives, the usual setting for multiple zeta functions. In addition, the Hopf algebra structure encoding the complicated combinatorics of Feynman integrals, uncovered by Connes and Kreimer, appears both in the theory of multiple zeta values and symbol calculations for pseudodifferential operators. Further research has shown that the connections are much more than coincidences, andthe work of Bloch, Connes, Esnault, Kreimer, Marcolli and others points towards the possibility of a noncommutative geometry explanation or a direct motives/quantum field theory connection.This is the first conference on this topic in the US. Since junior faculty and graduate students are encouraged to attend with partial NSF support, the schedule will include introductory lectures on the three conference areas and on Hopf algebras and multiple zeta functions. Other speakers will give research level talks on the conference areas, with a particular emphasis on their interactions.