EVENT DETAILS AND ABSTRACT

Title: From Prediction Theory to Arithmetic Progressions
Speaker: Hillel Furstenberg
Speaker Info: Northwestern University and Hebrew University, Jerusalem
Brief Description:
Special Note:
Abstract:

Going backwards from the ergodic theorem, we describe how a "statistically well-behaved" function on Z or R determines the dynamical mechanism giving rise to the sequence. This idea was developed systematically in connection with the problem of predicting from an individual "past". In this context the role of skew-product systems comes to light; this in turn leads to a discussion of distality. All these notions come together in the ergodic theoretic approach to the Szemeredi theorem on existence of long arithmetic progressions in sets of integers of positive density.