Mathematical Sciences: Algebra, Number Theory and Algebraic Geometry

该基金支持David Kazhdan教授和Benedict Gross教授作为主要研究人员和Boas Erez博士作为博士后助理进行研究。Kazhdan教授将研究张量范畴、量子群的表示和超流形上的积分理论。格罗斯教授将研究由群表示和三重积l函数构成的欧几里得格。埃雷兹博士将研究伽罗瓦模块理论中的问题。这是广义数论领域的研究。数论从整数和诸如整数能被整数整除之类的问题开始。它是数学中最古老的领域之一，最初纯粹出于审美原因而追求它。然而，在过去的半个世纪里，它已经成为开发计算机科学新算法和电子学新纠错码的重要工具。此外，为解决数论问题而开发的技术对理论物理也很有用，比如Kazhdan教授提出的量子群和无限维表示理论的研究，得到了这项资助。

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.