广州数学大讲坛第二期
第二十讲——中国矿业大学（北京）张俊强副教授学术报告（一）
题目：A survey of normal numbers from analytic view I
时间：2025年4月7日（周一）下午2:00-3:30
地点：理学实验楼314
报告人：张俊强 副教授
摘要：A real number x is normal in base b if every block of digits of the same length appears in the b-adic digit expansion of x with equal limiting frequency. While the concept is easy to define, proving that specific numbers are normal often requires deep and intricate methods. The study of normal numbers connects diverse areas of mathematics, including harmonic analysis, ergodic theory, and fractal geometry.
In this series of lectures, I will survey some key results and techniques in the study of normal numbers, explore the challenges posed by long-standing open problems, and present the recent resolution of a conjecture by Kahane and Salem regarding the properties of partially normal numbers. This work draws on methods from Fourier analysis, geometric measure theory, and probabilistic number theory. This is joint work with Professor Malabika Pramanik.
报告人简介：
张俊强，中国矿业大学（北京）副教授，博士毕业于北京师范大学，曾前往加拿大英属哥伦比亚大学（UBC）交流访问一年。研究方向为调和分析及其应用，在变指标的函数空间、椭圆算子相关的Hardy空间以及正规数等方面的研究取得了许多研究结果，其工作先后发表在Canad. J. Math., Publ. Mat.和JDE等国际知名杂志上。
