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).
