If the ring Z of integers is the union of finitely many residue classes a1(mod n1), . . . , ak(mod nk), then the system A = {as(mod ns)}k s=1 is called a cover of Z or a covering system. There are many problems and results on this topic initiated by Paul Erd ̈os. In this talk we give a survey of covering systems and covers of groups by left cosets, and also introduce the algebraic theory of periodic arithmetical maps motivated by the speaker’s research on covering systems. The talk is related to number theory, combinatorics, algebraic structures and special functions.

孙智伟，现为南京大学数学学院教授、博士生导师, 中国数学会组合与图论专业委员会副主任。其研究方向为数论与组合数学。

他获过多项荣誉与奖励，包括国务院政府特殊津贴、教育部首届青年教师奖、江苏省科技进步二等奖。

他在数论与组合、代数的交叉领域有许多创新成果, 迄今已在《Trans. Amer. Math. Soc.》等数学期刊上发表了两百多篇学术论文，还著有《数论与组合中的新猜想》、《Fibonacci数与Hilbert第十问题》等书。在限定未知数个数的整数环上Hilbert第十问题方面，他保持着世界最佳记录。他还提出了许多原创性数学猜想，引起了国际同行的广泛关注与研究。