报告标题:Sparse Hypergraphs: from Theory to Applications
报告人：葛根年教授 首都师范大学
报告时间：2022/11/19（周六)，16:00-17:00
报告地点：腾讯会议792603078
报告摘要:
For fixed integers $r,e,v$, an $r$-uniform hypergraph is said to be $(v,e)$-free or $(v,e)$-sparse if the union of any $e$ distinct edges of it contains at least $v+1$ vertices. The notion of sparse hypergraphs was initially introduced by Brown, Erd{\H{o}}s, and S{\'o}s in the 1970s. Since then, determining the upper and lower bounds on the maximum number of edges that can be contained in a sparse hypergraph with a given number of vertices has become one of the central problems in extremal combinatorics. A number of powerful methods from several disciplinaries, including combinatorics, probability, algebra, and number theory, have been applied to the study of sparse hypergraphs.
In this talk, we will introduce the recent developments on an important conjecture of Brown, Erd{\H{o}}s, and S{\'o}s on sparse hypergraphs, and discuss some unexpected applications of sparse hypergraphs to various topics in modern information sciences, including perfect and separating hash families (data security), locally repairable codes (data storage), and centralized coded caching schemes (data transmission).
报告人简介：葛根年，首都师范大学特聘教授，教育部长江学者、国家杰青、国家百千万人才、北京学者。长期从事组合数学、编码理论、信息安全、压缩感知、数据科学等数学与信息交叉科学研究。迄今共发表SCI论文200余篇，并被SCI他引2000余次，其中：60余篇发表在国际组合数学及信息学领域内顶尖刊物 《Journal of Combinatorial Theory, Series A》、《Journal of Combinatorial Theory, Series B》、《SIAM Journal on Discrete Mathematics》、《IEEE Transactions on Information Theory》及《IEEE Transactions on Signal Processing》上。自2014年爱思唯尔（Elsevier）发布“中国高被引学者（Most Cited Chinese Researchers）”榜单以来，一直进入榜单。同时，入选美国斯坦福大学发布的“2020全球前2%顶尖科学家（World's Top 2% Scientists 2020）”榜单、美国数学会发布的“高被引数学家（Most cited mathematicians）”榜单。曾任中国数学会组合数学与图论专业委员会主任、国际组合数学及其应用协会“Medals Committee Member”（全球共3人）。目前受邀担任国际组合数学界顶尖SCI期刊《Journal of Combinatorial Theory, Series A》、国际信息理论界顶尖SCI期刊《IEEE Transactions on Information Theory》、国际编码密码界权威SCI期刊《Designs, Codes and Cryptography》、国际组合设计界权威SCI期刊《Journal of Combinatorial Designs》、国际代数组合界权威SCI期刊《Journal of Algebraic Combinatorics》、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。曾获国际组合数学及其应用协会颁发的“Hall Medal”、中国青年科技奖、教育部自然科学二等奖、浙江省科学技术二等奖。
