INT 9406779 Gordon Technical Description: This project provides partial support for Brent Gordon, University of Oklahoma to be a guest scientist for four months at the Tata Institute for Fundamental Research (TIFR), School of Mathematics, Bombay and two months at the Mehta Research Institute, Allahabad, India. His research area is arithmetic algebraic geometry. The specific problems to be investigated focus on questions about algebraic cycles in algebraic-geometric varieties associated with automorphic forms. One goal of the research is to determine the Hodge structure, and verify the Hodge conjecture, for particular special constituents of these varieties. A second goal is to analyze and understand the groups of algebraic cycles modulo rational equivalence for some Kuga-Shimura varieties. Scope: This project will be very beneficial to Prof. Gordon's research by providing vital contact for an extended period with some exceptional Indian theorists with whom he has had limited contact at meetings and via e-mail. He anticipates significant interaction with two groups at TIFR and one group at the new Mehta Research Institute having common interests and expects that after the necessary incubation time specific plans for collaborations will develop. Indian scientists excel in theoretical mathematics and many mutual benefits may be expected to result from the interaction. Project corresponds with INT guidelines by supporting a new activity that benefits a U.S. scientist. ***
