走向现代数学学术报告 - 凡石磊教授（No. 794)

报告题目：Tiling, Exponential bases in non-Archimedean LCA groups

报 告 人：凡石磊 教授（华中师范大学）

邀 请 人：朱剑峰教授、鲍官龙副教授

报告时间：2025年5月27日 10:00

报告地点：东海岸校区-D实232

报告摘要：In this talk, we present our recent progress on Riesz bases and tiling problems in non-Archimedean harmonic analysis. We establish the existence of exponential Riesz bases for finite unions of balls in non-Archimedean locally compact Abelian groups, and demonstrate the non-existence of such bases for certain bounded sets. And we investigate translational tiling functions in the field $\mathbb{Q}_p$ of $p$-adic numbers, showing that any function that tiles $\mathbb{Q}_p$ by translation must be uniformly locally constant. As an application, we resolve a problem posed by H. Leptin and D. M\"uller by characterizing discrete sets that generate uniform partitions of unity. Furthermore, we explore the relationship between tiling and spectral properties in connection with the Fuglede conjecture, and prove that all tiles in the hybrid group $\mathbb{Q}_p \times \mathbb{Z}/2\mathbb{Z}$ are spectral sets.

专家简介：凡石磊，现任华中师范大学教授，博士生导师，2012年博士毕业于中科院数学所。从事非阿基米德域上动力系统、概率论及相关领域的研究工作，主要成果发表于Math. Ann., Adv.Math., Probab. Theory and Relat. Fields, Math. Z., J. London Math. Soc., J. Funct. Anal., J. Differential Equations, J. Dynam. Differential Equations，Sci. China Math.等国际学术期刊；先后主持博士后面上项目、国家自然科学基金青年项目、国家自然科学基金委国际合作与交流项目、国家自然科学基金面上项目、霍英东青年教师基金项目等。