Interdisciplinary Study of Conformal Field Theory-Mathematics and Physics

最近，数学与物理学发生了广泛的相互作用，特别是与量子场论(QFT)、弦理论、保形场理论和Seiberg-Witten理论的思想的互动。这些理论为我们提供了对基本物理定律最深刻的理解。数学，特别是代数和微分几何，为这些理论提供了正确的框架，数学技术使物理学家能够建立他们的许多结果，特别是在弦理论和共形场论中。另一方面，物理学家，如Witten，Candelas和其他许多人，已经利用物理思想发现了许多真正令人惊叹的数学关系。然而，很少有数学家完全熟悉物理学的概念。我们必须训练我们的学生理解这些理论。吉赛克教授的目标是学习共形场理论，这是一个非常基本的理论，也是弦理论的基石。在此基础上，他将开发一门课程，让渴望学习这些理论的数学研究生能够接触到。在研究方面，Gieseker教授最近的研究一直是无限维可积系统的形变理论，这与保形场理论密切相关。因此，理解保形场理论将丰富他的研究。在这个项目中，吉赛克教授将与加州大学洛杉矶分校物理系的埃里克·德霍克教授合作。该IGMS项目由重大计划多学科活动办公室(OMA)和数学科学处(DMS)共同支持。

Mathematics has recently seen extensive interaction with physics, especially with the ideas of quantum field theory (QFT), string theory, conformal field theory and Seiberg-Witten theory. These theories provide our deepest understanding of basic physical laws. Mathematics, especially algebraic and differential geometry, has provided the correct framework for these theories, and mathematical techniques have enabled the physicists to establish many of their results, especially in string theory and conformal field theory. On the other hand, physicists, such as Witten, Candelas and many others, have discovered many truly amazing mathematical relationships using physical ideas. However, few mathematicians are fully conversant with the concepts of physics. It is imperative that we train our students to understand these theories. Professor Gieseker's objective is to learn conformal field theory, which is a very basic theory which is also a building block for string theory. From this, he will develop a course which will be accessible to mathematics graduate students, who are eager to learn these theories. On the research side, Professor Gieseker's recent research has been in the deformation theory of infinite dimensional integrable systems, which is closely connected to conformal field theory. So understanding conformal field theory will enrich his research. In this project, Professor Gieseker will collaborate with Professor Eric D'Hoker of the UCLA Physics Department. This IGMS project is jointly supported by the MPS Office of Multidisciplinary Activities (OMA) and the Division of Mathematical Sciences (DMS).