题目：Two Local-Global Theorems related to Covers of the Integers

报告人：孙智伟，南京大学

时间：2020年12月1日（星期二）16：00-17：00

地点：东区第五教学楼5205教室

摘要：A system A = {a_s + n_s Z: 1≤s≤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. Erdös in the 1930s. Erdös ever conjectured that A is a cover of Z whenever it covers 1, ..., 2^k.

    In this talk we introduce the speaker's two local-global theorems arising from his study of covers of Z. One of them states that if  ψ_1, ...,  ψ_k are maps from Z to an additive abelian group G with positive periods n_1, ..., n_k respectively then the sum function  ψ= ψ_1+... +  ψ_k is a constant function whenever  ψ(x) =  ψ(x+1) = ... =  ψ(x+|S|-1) for some x∈ Z, where S is the union of {r/n_s: 0≤r≤n_s-1} for 1≤s≤k. 

报告人介绍: 孙智伟, 南京大学数学系教授、数学系数学与应用数学专业主任, 中国数学会组合与图论专业委员会副主任，其研究方向为组合数论与加法组合。2005年获国家杰出青年科学基金，2010年获国务院政府特殊津贴。他是《Journal of Combinatorics and Number Theory（组合与数论杂志）》的创刊主编, 《Electronic Research Archive》编委。他在组合与数论交叉领域成果卓著， 并因提出的许多原创性数学猜想广受国际数学界关注。