Title: Furstenberg's tower and application to number theory

Date：12月27日 3:10-4:10pm

Speaker: Wang Feng, Peking University

Abstract:Furstenburg had construced a tower for a general dynamical system acted by Z^n in a meature preserving way.This strcture theorem can prove the so called muliplier recurrence theorem.As a consequence, we get that under density condition(a subset has positive density roughly means that it contains a definite portion of [0,N] for any N),there is a arithmetical progress of any length.The proof of the theorem is purly ergodic.But we will still mention the connections to the prime case（a theorem due to Ben Green&Terrence Tao):it says that we still have a arithmetical progress of any length in the prime numbers.