报告人 ：赖俊杰（旧金山州立大学）

时间：2023年06月02日 10:00--

Zoom ID：899 9151 8372   Code: 415196

ZOOM Link https://sfsu.zoom.us/j/89991518372?pwd=VytqOGE5RFhZRDF3TnlURDRlQ0ppUT09

摘要：A pattern is called universal in another collection of sets, when every set in the collection contains some linear and translated copy of the original pattern. Paul Erdős proposed a conjecture that no infinite set is universal in the collection of sets with positive measure.

In this talk, we explore an analogous problem in the topological setting. Instead of sets with positive measure, we investigate the collection of dense  sets and in the collection of generic sets (dense G-delta and complement has Lebesgue measure zero). We refer to such pattern as topologically universal and generically universal respectively. We will show that Cantor sets on R^d are never topologically universal and Cantor sets with positive Newhouse thickness on R^1 are not generically universal. This gives a positive partial answer to a question by Svetic concerning the Erdős similarity problem on Cantor sets. Moreover, we also obtain a higher dimensional generalization of the generic universality problem.

简介：赖俊杰（Chun-Kit Lai）, 现为美国旧金山大学教授，2012年博士毕业于香港中文大学数学系，导师为刘家成（Ka-Sing Lau）教授，2012-2014在加拿大McMaster大学做博后，合作导师为 J.P. Gabardo 教授。 主要研究兴趣有：Fourier Analysis and Harmonic Analysis, Fractal Geometry, Tiling Theory, Frame Theory. 到目前为止，已在Adv.Math., J.Funct.Anal., Tran.Amer.Math.Soc, J.Math.Pure.Appl.等国际高水平数学杂志发表论文20余篇.

邀请人：罗军

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