北航数学论坛学术报告

--几何测度论与相关领域讨论班

Capacities and dimensions for random sets in metric spaces

Arnaud Durand 副教授

（巴黎萨克雷大学）

报告时间：14：00-15：00，2025-04-25（星期五）

报告地点：学院路校区新主楼F122

内容简介：In a metric space, we study random sets that almost surely intersect every compact set with positive capacity for a given potential. This property implies an a priori lower bound on the size of the random set, and even on its intersection with any deterministic set. It is also related to Falconer's large intersection property. We consider the example of sets written as limsup of random balls and show that their dimension is linked to the multifractal properties of an underlying intensity measure. This will allow us to establish connections with problems of random coverings, such as Dvoretzky's problem, and with dynamical Diophantine approximation.

报告人简介：报告人Arnaud Durand，法国巴黎萨克雷大学（原巴黎第十一大学）副教授，研究方向主要涉及几何测度论、分形几何、动力系统、调和分析以及数论。文章多次发表在JEMS、PTRF、Ann. Statist、CMP、Advances等国际顶刊上，并多次受邀在分形几何、概率论与动力系统大型国际学术会议和短期学术交流活动中做大会报告。

邀请人：梁湘玉