Mathematical Sciences: Algebra, Number Theory and Algebraic Geometry

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This grant supports the research of Professors David Kazhdan and Benedict Gross as principal investigators and Dr. Boas Erez as a post-doctoral associate. Professor Kazhdan will work on tensor categories, the representation of quantum groups and the theory of integration over supermanifolds. Professor Gross will study Euclidean lattices constructed from group representations and triple product l-functions. Dr. Erez will study problems in Galois module theory. This is research in the field of number theory broadly conceived. Number theory starts with the whole numbers and questions such as the divisibility of one whole number by another. It is among the oldest fields of mathematics and it was originally pursued for purely aesthetic reasons. However, within the last half century, it has become an essential tool in developing new algorithms for computer science and new error correcting codes for electronics. Moreover, techniques developed for their applications to problems in number theory have become useful for theoretical physics - as in the proposed research in quantum groups and infinite dimensional representation theory of Professor Kazhdan supported by this grant.