A Szemeredi-type theorem for free groups
Student No.:100
Time:Tue 16:30-17:30, Dec.25
Instructor:Hillel Furstenberg  
Place:Lecture Hall, Jin Chun Yuan West Bldg.
Starting Date:2018-12-25
Ending Date:2018-12-25

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.

About speaker:
Hillel Furstenberg now works at The Hebrew University of Jerusalem as professor. He is not only the member of the Israeli academy of sciences and the academy of humanities, but also the member of American academy of arts and sciences. He once taught in Princeton University and other universities. He mainly focuses on probability theory, ergodic theory, number theory and lie group. Here are the rewards he received, the Israel Prize and Harvey Prize from Technion in 1993 and the Wolf Prize in Mathematics in 2006.
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。
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)