Japan Long Term Visit: "Tau-Functions for Dirac Operators"

这笔奖金将支持加州大学戴维斯分校数学系的Craig A.Tracy教授及其研究生Morris Beatty先生为期两个月的为期六个月的长期访问，以与京都大学数学科学研究所(RIMS)的T.Miwa教授进行合作研究项目。他们的合作研究将包括继续研究由流形上自由费米子的完整量子场论产生的等单向t函数。这对于理解和澄清双曲空间中量子场论的相的性质将是重要的；它应该允许对零曲率极限进行透明的讨论。这项研究的结果应该对完整量子场、可积系统和微分几何有意义。这一研究对于数学物理中的等单数问题具有重要意义。这两个群体在各自的领域都是备受尊敬的专家。RIMS是研究人员开展研究的理想机构。在京都，他们将与t型函数概念的发明者--佐藤美纪夫教授、三和哲二教授和金保道夫教授一起工作。他们都以对完整量子场的创新方法和相关的等向单线变换而闻名。此外，该研究所还有许多黎曼曲面理论方面的专家。预计，在该奖项到期后，研究人员之间的合作可能会继续下去。

This award will support two months of a six-month, long-term visit by Professor Craig A. Tracy and his graduate student Mr. Morris Beatty of the Department of Mathematics at the University of California, Davis, to Japan for a cooperative research project with Professor T. Miwa, Research Institute for Mathematical Sciences (RIMS) at Kyoto University. Their collaborative research will involve continued investigation into isomonodromic t-functions that arise from a holonomic quantum field theory of free fermions on manifolds. This will be important in understanding and clarifying the nature of phases for a quantum field theory in hyperbolic space; and it should permit a transparent discussion of the zero curvature limit. Results of the research should have implications for holonomic quantum fields, integrable systems and differential geometry. The research is of fundamental importance with respect to isomonodromy problems in mathematical physics. Both groups are well-respected experts in their field. RIMS is the ideal Institute for the researchers to carry out their research. At Kyoto they will be working with the inventors of the notion of a t-function; Professors Mikio Sato, Tetsuji Miwa and Michio Jimbo. They are all known for their innovative approach to holonomic quantum fields and associated isomonodromic transformations. In addition, there are many experts in Riemann surface theory at the Institute. It is expected that, following the expiration of this award, collaborations between the researchers are likely to continue.