Professor Greenberg will continue his investigations of the properties of Selmer groups and their connections with values of certain L-functions that occur naturally in number theory and algebraic geometry. Three seemingly separate fields of modern mathematics meet in this project: Number Theory, Algebraic Geometry, and Analysis. Number Theory means the study of the whole numbers, static and discrete; Algebraic Geometry began with the study of the relations and motions of constructs like lines and planes, but has taken on an ever more abstract and algebraic tone in recent years; Analysis refers to that broad region of mathematics that is related to Calculus. That modern arithmetical algebraic geometry is drawing from these three fields and simultaneously making contributions to them is one of the most exciting developments in mathematics today.
