Fuglede's conjecture in Q_p
报 告 人:: 凡石磊
报告地点:: 综合教学楼107室
报告时间:: 2018年08月21日星期二10:00-11:00

I will report on our recent progress in studying Fuglede's conjecture in the filed Q_p of p-adic numbers.  We proved that Fuglede's conjecture concerning spectral sets and tilings holds in the field of p-adic numbers, i.e. a Borel set of positive and finite Haar measure is a spectral set if and only if it tiles the space by translation, although the conjecture remains open in the field of real numbers. Our study is based on the investigation of a convolution equation of the form f * \mu =1, where \mu is a measure supported by a discrete set and f is a non-negative integrable function. I. J. Schoenberg's result concerning the p^n-th roots of unity plays a crucial role. These are joint works with Ai-Hua FAN, Lingmin Liao and Ruxi Shi.

发 布 人:吴双 发布时间: 2018-08-19
凡石磊,华中师范大学数学与统计学学院副教授,2003年-2007年就读于吉林大学数学学院,2012年在中科院数学与系统科学院数学所获博士学位,导师是王跃飞研究员,2012-2014年在中科院数学与系统科学院数学所开展博士后工作,2014年6月起任华中师范大学数学与统计学学院副教授至今。主要从事遍历论、复分析及复动力系统、代数动力系统等领域的研究,曾多次赴法国开展学术交流合作,目前已在 J. Funct. Anal. Adv. Math. J. Differential Equations J. Number Theory等著名杂志发表文章十余篇,2017年入选湖北省“楚天学者计划”楚天学子。