深圳技术大学大数据与互联网学院数学系学术报告（一）

报告主题：Intermediate Dimensions

报 告 人：Dr. Amlan Banaji (University of St Andrews)

报告时间：2022年10月21日（星期五），下午17:00—18:00 

报告地点：（Zoom）会议号：760 812 5593，密码：standrews

邀 请 人：陈海鹏 博士

摘    要：

The intermediate dimensions are a family of dimensions which lie between two familiar notions of fractal dimension, namely the Hausdorff and box dimensions. After defining the intermediate dimensions, we will describe the form they take for several different classes of fractal sets. In particular, we will consider polynomial sequence sets, the graph of the popcorn function, and self-affine Bedford-McMullen carpets. We will then state a necessary and sufficient condition which determines whether a given function can be realised as the intermediate dimensions of a subset of Euclidean space. In this survey-style talk, results from several different projects will be mentioned, three of which are joint with Haipeng Chen, Istvan Kolossvary and Alex Rutar respectively.

报告人简介：

Dr. Amlan Banaji，本科毕业于剑桥大学，硕士毕业于圣安德鲁斯大学，并荣获” Postgraduate Gray Prize” ，现为圣安德鲁斯大学博士，导师为Prof. Jonathan Fraser与Reguis Prof. Kenneth Falconer，研究领域为分形几何，研究课题包括分形集的中间维数(intermediate dimensions)等，近年来于Trans. Amer. Math. Soc., Ann. Fenn. Math.等高水平学术杂志发表论文3篇。