应我院邀请，国防科技大学数学系周悦博士于2019年4月4日访问我院，并做了题为“On the nonexistence of abelian Cayley graphs of diameter 2 meeting the Moore-like bound” 的学术报告，报告涉及了经典的图论组合、离散几何、编码等课题。图论及其应用相关方向教师与研究生参与了报告并交流，杨卫华博士主持报告。
周悦博士现任国防科技大学数学系副研究员，获德国“洪堡”学者资助，2016年度Kirkman奖章获得者。在Adv. Math, JCTA等著名期刊上发表SCI论文近30篇，主持国家自然科学基金面上项目1项，青年项目1项，获湖南省优秀青年基金资助。
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.