9700477 Gross This award supports research of Pavel Etingof, David Kazhdan and Benedict Gross in several areas of the theory of quantization, quantum groups, special functions, representation theory and number theory. Etingof will work on the new theory of dynamical quantum groups and special functions, and continue the joint work with Kazhdan on quantization and the theory of quantum groups. Kazhdan will continue his work on the discrete series for GL(n) and on minimal representations over local fields and will work on the theory of algebraic integration. Gross will continue his work on a construction of motives with Galois gpoup G2, via an exceptional theta correspondence, and will study Galois representations associated to "algebraic" automorphic forms. This project involves research in Algebra and Number Theory. Algebra can be though of as the study of symmetry in the abstract. As such, Algebra has direct applications to areas of physics and chemistry. In particular, the modern theory of gauge fields in physics uses algebra extensively. Number Theory has its historical roots in the study of the whole numbers, addressing such questions as those dealing with the divisibility of one whole number by another. It is among the oldest branches of mathematics and was pursued for many centuries for purely aesthetic reasons. Modern Number Theory and Algebra are very technical and deep. However, within the last half century, they have become indispensable tools in diverse applications in areas such as data transmission and processing, and communication systems.
