Mathematical Sciences: Research in Number Theory and Automorphic Forms

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This award supports the research in Automorphic Forms of Professor Michael Harris of Brandeis University. Dr. Harris's research project is to study the number-theoretic properties of holomorphic and nonholomorphic automorphic forms, and relations with special values of L-functions. His principal tool for attack of his chosen problems will be the cohomology of the toroidal compactification of Shimura varieties. 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.