9401466 Rogawski This award funds the investigations of Professor Jonathan Rogawski in the theory of automorphic representations and its relations with number theory. The work has three objectives; first to construct motives for Hilbert modular forms of a particular weight, second to prove a conjecture relating the existence of Heisenberg models to the multiplicity pairing, and finally to construct a correspondence between certain representations of unitary groups with representations of the general linear group. This research is in a part of number theory generally known as the Langland's program. Number theory is the study of the properties of the whole numbers and is the oldest branch of mathematics. From the beginning problems in number theory have furnished a driving force in creating new mathematics in other diverse parts of the discipline. The Langland's program is a general philosophy that connects number theory with calculus; it embodies the modern approach to the study of whole numbers. Modern number theory is very technical and deep, but it has had astonishing applications in areas like theoretical computer science and coding theory.
