Mathematical Sciences: Automorphic Forms of Galois Type, andthe L-functions of Some Simple Moduli Varieties

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This award supports the research on Automorphic Forms of Professor Dinakar Ramakrishnan of the California Institute of Technology. Dr. Ramakrishnan plans to continue his work on cusp forms of arithmetic type on GL(2), and to investigate certain ensuing problems concerning the Shimura varieties attached to GSp(4) and U(4). He also plans to study the cohomology and cycle classes on these varieties with a view to finding examples of the expected relationship to poles and zeros of L-functions. Non-Euclidean plane geometry began in the early nineteenth century as a mathematical curiosity, but by the end of that century, mathematicians had realized that many objects of fundamental importance are non-Euclidean in their basic nature. The detailed study of non-Euclidean plane geometries has given rise to several branches of modern mathematics, of which the study of Modular and Automorphic Forms is one of the most active. This field is principally concerned with questions about the whole numbers, but in its use of Geometry and Analysis, it retains connection to its historical roots.