Conference: Motives, Quantum Field Theory and Pseudodifferential Operators

2008年6月2-14日，波士顿大学将主办“动机、量子场论和伪微分算子”会议。本次会议将以介绍和高级讲座为特色，介绍这些已建立的领域之间迅速发展的关系。由于这些研究领域的基本工具有很大的不同，因此需要会议不同方面的专家对他们的主题进行概述，并指出这些主题之间的相互作用。演讲者和参与者已被邀请来自美国和欧洲。来自这三个领域的30多位顶尖数学家已经同意参加会议，其中包括Spencer Bloch、Alain Connes、Alexander Goncharov、Dirk Kreimer和Richard Melrose。参加这次会议的预计大约有75 - 100名数学家和数学物理学家。动机、量子场论和伪微分算子这三个领域作为独立的领域已经很好地建立和活跃，但直到过去十年，它们一直被视为本质上脱节的企业。动机理论是由格罗滕迪克在20世纪60年代发展起来的，它是一个包含多种上同调理论的算术代数几何体系。摄动量子场论最早出现在1945年左右，用来解释量子电动力学和其他场论的实验结果，它在很大程度上依赖于费曼积分的计算。最后，伪微分算子理论，起源于20世纪60年代，是一个框架来处理所有经典微分算子，格林算子和热算子在一个设置。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子的出现。多个zeta值作为费曼积分值的意外出现，表明量子场论与动机之间存在着深刻的联系，动机是多个zeta函数的通常设置。此外，由Connes和Kreimer发现的编码费曼积分复杂组合的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，而Bloch、Connes、Esnault、Kreimer、Marcolli和其他人的工作指出了非交换几何解释或直接动机/量子场论联系的可能性。这是美国首次召开有关这一主题的会议。由于鼓励初级教师和研究生在部分NSF支持下参加会议，日程安排将包括三个会议领域的介绍性讲座，以及Hopf代数和多重zeta函数。其他发言者将就会议领域进行研究层面的讨论，特别强调它们之间的相互作用。

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.