广州数学大讲坛第十二期
第一百一十二讲——湖北大学高翔博士学术报告
题目：Fourier analysis of fractal measures and Diophantine approximation.
时间：2023年12月21日（周四）下午14：30——15：30
地点：理科南楼108
报告人：高翔博士
摘要: It is well known that Lebesgue almost everywhere points are normal numbers. Firstly, we will give some background on this topic, and survey some recent results on normal numbers on fractals. We will discuss how to use some powerful tools from probability theory, harmonic analysis, measure rigidity in ergodic theorem, to study the problems of normality on fractals.
The second part is devoted to investigating the Fourier transform of fractals measure, including the Fourier decay estimate of some self-similar measure with special algebraic contractive ratios, and of projected measures of product of Bernoulli convolutions under different directions parameters. We study various kinds of conditions which are imposed on fractal measures to guarantee that generic points are absolutely normal. Our main goal is to show how we use Diophantine approximation tools, such as Thue-Siegel-Roth theorem and Linear forms in logarithms to deal with the Fourier analytic behaviors of some fractal measures.
Finally, we will discuss some work we are working on and several open problems we plan to go further.
报告人简介：
高翔，博士，就职于湖北大学，先后毕业于武汉理工大学，华中科技大学和武汉大学（法国亚眠大学联培博士）。访问加拿大英属哥伦比亚大学（2022.7-2023.7），芬兰奥卢大学（2019.11-2019.12），研究方向为度量数论、动力系统、傅里叶分析在分形中的应用，主要关注丢番图逼近，和分形测度的傅里叶变换及其在分形几何上的应用。
