Workshop on P-Adic Dynamics

Amherst College, Amherst MA

Investigators

Abstract

The emerging field of p-adic dynamics has received a sizable amount of attention from around the world, including a course at the College de France given by J.-C. Yoccoz in 2000. The subject promises new developments in the near future for research in number theory, topological dynamics, and ergodic theory. In this three-day workshop scheduled for May, 2005, participants with strengths in these three fields of mathematics will exchange ideas via lectures and discussions concerning the work which has appeared up to now, helping to generate ideas for future research in this subject. Even in the relatively few years of its existence as a research area, p-adic dynamics has attracted interest from a number of dynamicists and ergodic theorists for its parallels and contrasts with complex dynamics, as well as from number theorists for its applications to the study of iteration of functions over global fields. A number of fundamental theorems and surprising pathological examples have already been discovered, while at the same time several conjectures have emerged as key open questions in the subject. Ergodic theory and dynamical systems are relatively young subjects which evolved to study the chaotic and seemingly random behavior of nonlinear systems. Their descriptions of chaotic behavior have led to myriad applications in physics and engineering. On the other hand, number theory is a subject which has been studied since ancient times, but whose beauty and intricacy has kept it alive and strong into the present day, where it has even found applications in cryptography and coding theory. Now, p-adic dynamics provides an opportunity for these vibrant subjects to interact in a way that ultimately has the potential to provide further understanding of all these applications.