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.
