组合数学和代数编码讲座—— Covers of the Integers by Residue Classes and their Extensions to Groups

报 告 人：孙智伟教授（南京大学）

报告时间：2024年10月18日周五下午3:00-4:00

报告地点：海纳苑2幢820

摘  要：A system A={a_s+n_sZ: s=1,2,...,k} of k residue classes is called a cover of Z if any integer belongs to one of the k residue classes. This concept was introduced by P. Erdos in the 1950s. Erdos ever conjectured that A is a cover of Z whenever it covers 1,...,2^k. In this talk we introduce some basic results on covers of Z as well as their elegant proofs. We will also talk about covers of groups by finitely many cosets, give a proof of the Neumann-Tomkinson theorem, and introduce progress on the Herzog-Schonheim conjecture and the speaker's disjoint cosets conjecture.

报告人简介：孙智伟，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，例如：教育部首届青年教师奖、国家杰出青年科学基金与国务院政府特殊津贴。他在数论与组合、代数的交叉领域有许多创新成果, 已在国内外重要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。他还提出了许多原创性数学猜想，引起了国际同行的关注与研究。