A Szemeredi-type theorem for free groups

组织者 Organizer:Hillel Furstenberg
时间 Time: 周二16:30-17:30,2018-12-25
地点 Venue:清华大学近春园西楼三层报告厅

摘要 Abstract

The theorem of Szemeredi on existence of arbitrarily long arithmetic progressions in sets of integers of positive density is known to be equivalent to a "multiple recurrence" theorem for ergodic measure preserving dynamical systems. An analogous theorem for non-amenable groups can be demonstrated by introducing the notion of a "stationary group action" where measure need not be preserved. Based on this one can formulate conditions on subsets of an arbitrary group that guarantee existence of arbitrarily long geometric progressions. These conditions can be made explicit for a finitely generated free group.

报告人简介 Profile

Hillel Furstenberg,以色列希伯来大学教授,以色列科学院和人文学科院院士,美国国家科学院院士,沃尔夫数学奖的得主。Harry Furstenberg教授曾在普林斯顿大学等多个高校担任教授。他的研究方向为概率论和遍历理论,以及数论和李群。

学术荣誉:

1993年 获以色列奖 (Israel Prize

1993年 获以色列理工颁发的哈维奖 (Harvey Prize from Technion

2006年 获沃尔夫数学奖 (Wolf Prize in Mathematics