應我院邀請，國防科技大學數學系周悅博士于2019年4月4日訪問我院，并做了題為“On the nonexistence of abelian Cayley graphs of diameter 2 meeting the Moore-like bound” 的學術報告，報告涉及了經典的圖論組合、離散幾何、編碼等課題。圖論及其應用相關方向教師與研究生參與了報告并交流，楊衛華博士主持報告。
周悅博士現任國防科技大學數學系副研究員，獲德國“洪堡”學者資助，2016年度Kirkman獎章獲得者。在Adv. Math, JCTA等著名期刊上發表SCI論文近30篇，主持國家自然科學基金面上項目1項，青年項目1項，獲湖南省優秀青年基金資助。
報告摘要:
In 1968, Golomb and Welch conjectured that Zn cannot be tiled by Lee spheres with a fixed radius r ≥ 2 for dimension n ≥ 3. Besides its own interest in discrete geometry and coding theory, if we restrict this conjecture to the lattice tiling case it is also equivalent to the nonexistence of abelian Cayley graphs archiving the Moore-like bound for the cardinality of vertices. A question on the existence of abelian Cayley graphs achieving this upper bound except for some trivial examples has been proposed independently in the context of graph theory for many years.
In this talk, I will first give a brief survey of known results. Then I will sketch a proof on the nonexistence of lattice tilings of Zn by Lee spheres of radius 2 with n ≥ 3. As a consequence, we will see that the order of any abelian Cayley graph of diameter 2 and degree larger than 5 cannot meet the abelian Cayley Moore-like bound. This talk is based on a recent joint work with Ka Hin Leung.
