深圳技术大学大数据与互联网学院数学系学术报告（四）

报告标题：Sullivan's dictionary, conformal dynamics, and Assouad type dimensions

报 告 人：Prof. Jonathan Fraser

报告时间：2022年11月10日（星期四），18：00—19：00

报告地点：（Zoom）会议号：841 7271 6246 ；密码：standrews

邀 请 人：陈海鹏 博士

摘 要：

The Sullivan dictionary provides a conceptual framework to compare the actions of Kleinian groups and the dynamics of rational maps. Both of these settings generate beautiful fractal sets and the dictionary provides a particularly strong correspondence concerning the dimension theory of these sets. For example, restricting to the geometrically finite setting, in both cases there is a 'critical exponent' which returns the Hausdorff, box, and packing dimensions of the associated fractal set. We show that by expanding the family of dimensions considered to include the 'Assouad type dimensions' a richer dimension theory emerges. This allows us to draw new comparisons, and also provide novel discrepancies, between the Kleinian and rational map settings. This is joint work with Liam Stuart.

报告人简介：

Prof. Jonathan Fraser，苏格兰圣安德鲁斯大学教授，数学系分析课题组组长，博士生导师，研究领域包括分形几何、几何测度论、动力系统、遍历理论、双曲几何学等，在Adv. Math., Tran. Amer. Math. Soc., IMRN, ETDS, Math. Z., Indiana Univ. Math. J.等高水平学术期刊发表60余篇论文，著有《Assouad dimension and Fractal Geometry》学术专著一部，学术成果被引次数超过1100次，任《Proceedings of the Royal Society of Edinburgh (Section A)》主编，荣获Thomas Makdougall Brisbane Medal， RSE Young Academy of Scotland等学术奖励，多次受邀在英国、欧洲、美国等地区进行学术报告及学术交流。