This award supports the research on p-adic Galois repre- sentations of Professor Shankar Sen of Cornell University. Dr. Sen's project consists of two parts: the first is to relate the generalized Hodge-Tate structure of the representation to the various p-adic liftings of global Galois representations over the prime field in characteristic p. The other part is to extend previous work of Dr. Sen that described p-adic field extensions by means of certain semi-linear integral representations of p- power cyclic groups. Except for counting, number theory, which is the study of the properties of the whole numbers, is the oldest branch of mathematics. In modern days, problems in number theory have furnished the driving force to creation of new mathematics in the fields of pure algebra, analysis, and geometry; some of the most recent and most astonishing applications of number theory have appeared in theoretical computer science and coding theory.
