Integer valued polynomials in topology and number theory

This research project investigates algebras of integer valued polynomials and their applications in algebraic topology and number theory. The central objects of study, algebras of polynomials determined by integrality conditions, have been of interest toalgebraists for at least 100 years and have been a rich source of examples and structuralresults. Their occurence in algebraic topology and number theory is more recent, dating from the 1970's, and motivates the study of their computational properties. In this project methods for constructing regular bases for such algebras are developed and these will beused to assist in the computations of stable homotopy groups in topology and of rings of endomorphisms of formal groups in number theory.