报告名称：Diophantine approximation with exponential speed

报告专家：廖灵敏

专家所在单位：武汉大学

报告时间：2023-12-05下午四点-六点

报告地点:威廉希尔201

专家简介：

廖灵敏，2008年获法国Picardie大学及武汉大学博士学位。2010年获法国东巴黎大学终身教职。2017年获Habilitation。2021年12月国家海外引进高层次人才青年项目。2022年7月入职武汉大学，任教授博士生导师。主要从事分形几何，动力系统，度量数论等方面的研究。在J.Eur.Math.Soc., Math.Ann., Adv. Math., 等期刊发表论文四十余篇。

报告摘要：

We aim at calculating the Hausdorff dimension of the set of the couples (x,y) in the unit square such that |qx-p_1|<q^{-t} and |qy-p_2|<e^{-q} holds for infinitely many integer triples (q, p_1,p_2) with q>0, where t>0 is a positive real number. Such a study is a generalization of the classical simultaneous Diophantine approximation by replacing the approximation speed q^{-v} (v>0) for the second coordinate y to the exponential speed e^{-q}. The upper bound can be easily deduced from the existing results. For the lower bound, we need to develop the Mass Transference Principle of Wang and Wu (Math. Ann 2021) to incorporate the unbounded setup. This is a joint work with Bing Li, Baowei Wang, Sanju Velani and Evgeniy Zorin.