CAREER: Dynamical Systems on Homogeneous Spaces and Applications to Number Theory

Brandeis University, Waltham MA

Investigators

Abstract

Abstract DMS 0238463 D Kleinbock(Brandeis): Career The research component of the project deals with algebraic dynamical systems and their applications to number theory. A dynamical system here stands for an abstract set of points together with an evolution law which governs the way points move over time. It turns out that many problems concerning simultaneous approximation of real numbers by rational numbers can be cast in terms of the behavior of certain orbits, and various phenomena related to the theory of integer equations or inequalities can be better understood once they are phrased in dynamical systems language. Furthermore, systems that arise in this context are of algebraic nature, which makes it possible to use a wide variety of sophisticated tools for their investigation. The educational component consists of several ingredients: developing new `creative thinking' courses and supervising summer research projects for both undergraduate and graduate students, and maintaining an introductory-style interdisciplinary seminar. The goals are to engage students in challenging research projects, encourage non-standard independent thinking, and to expose them to a broad spectrum of current mathematical research.