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首都师范大学葛根年教授学术报告会通知


应数学与计算科学学院及广西高校数据分析与计算重点实验室邀请,首都师范大学葛根年教授将于1213日来js金沙所有网址讲学,欢迎全校师生踊跃参加。学术报告具体安排如下:

学术报告题目:Sparse hypergraphs: from Theory to applications
时间:20171213日(周三)下午1630
地点:金鸡岭校区F2
主讲人:葛根年教授

报告摘要:More than forty years ago, Brown, Erdos and Sos introduced the function fr(n; v; e) to denote the maximum number of edges in an r-uniform hypergraph on n vertices which does not contain e edges spanned by v vertices. They posed a well-known conjecture: nk??o(1) < fr(n; e(r ?? k) +k + 1; e) = o(nk) holds for all integers r > k _ 2, e _ 3. Note that for r = 3; e = 3; k = 2, this conjecture was solved by the famous Ruzsa-Szemer_edi's (6,3)-theorem. We add more evidence for the validity of this conjecture. On one hand, we use the hypergraph removal lemma to prove that the upper bound is true for all _xed integers r _ k + 1 _ e _ 3. On the other hand, we use tools from additive number theory to show that the lower bound is true for r _ 3; k = 2 and e = 4; 5; 7; 8.

We also use the theory of sparse hypergraphs to attack several open problems and conjectures in cryptography and coding theory. For example, we use the (6,3)-theorem to solve a conjecture ofWalker and Colbourn on perfect hash families. This conjecture had been open for ten years and traditional methods seem to have limited e_ect on it. We also use the (6,3)-free hypergraphs to construct two classes of placement delivery arrays which are useful for centralized coded caching. The complexity of the PDAs is improved from exponential to sub-exponential.

报告人概况:

葛根年,首都师范大学特聘教授,教育部长江特聘教授、国家杰青、国家百千万人才、北京学者。研究方向:组合数学与信息交叉科学。在国际组合数学及信息学领域内顶尖刊物《组合论杂志》、《SIAM离散数学》、《IEEE信息论汇刊》、《IEEE信号处理汇刊》等期刊上发表SCI论文180余篇,并被SCI引用1500余次。现任中国组合数学与图论学会副理事长、国际组合数学及其应用协会FellowCouncil Member。目前受邀担任国际组合设计界权威SCI期刊《J. Combinatorial Designs》、国内权威SCI期刊《中国科学:数学》、国内SCI期刊《高校应用数学学报》的编委。


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