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时间：2016-03-28 18:02:21 来源： 作者：数学学院

报告题目：Commom difference sets, higher order recurrence sets and related problems

报 告 人：黄文（中国科技大学数学科学学院）

报告时间：2016年4月8日（周五）下午16:00

报告地点：数学学院学术报告厅（数学楼315室）

报告摘要：

It is believed that a “big” subset of natural numbers should contain “good” linear structures, for example arbitrarily long arithmetic progressions (AP). Szemerdi's Theorem asserts that every positive upper Banach density subset of natural numbers has this property. In this talk, we will consider the structure of all common differences of AP with length k+1 appeared in a “big” subset of natural numbers. By the Furstenberg correspondence principle, the common difference set of AP of a syndetic (or positive upper Banach density) subset are related to the higher order recurrence sets in dynamical systems. It is shown that a higher order recurrence sets is an almost Nil Bohr-sets, and Nil Bohr-sets could be characterized via generalized polynomials. Hence the common difference set of AP of a syndetic (or positive upper Banach density) subset is an almost Nil Bohr-sets, which could be characterized via generalized polynomials. Some related problems in dynamical system (for example multiple ergodic average problem) will be also discussed. Finally we will review some progress on the difference set of primes.

报告人简介：黄文，从事拓扑动力系统与遍历理论研究，主要涉及熵理论、混沌理论以及系统回复属性。与合作者一起在零熵系统及其不变量、混沌的层次与产生机制、熵的局部化理论、回复属性与传递系统分类等方面取得进展，已在《Memoirs of the American Mathematical Society》、 《Adv.Math.》、《Ann. Probab.》、 《Comm.Math.Phys.》、《J. Math. Pures Appl.》、 《J.Funct.Anal.》、《Ergodic Theory Dynam. Systems》、《Trans.Amer.Math.Soc》、《中国科学A辑》等国内外杂志发表学术论文50余篇。入选2005年度全国优秀博士学位论文，入选2004年度教育部“新世纪优秀人才支持计划”，获2012年国家杰出青年基金。

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