报告题目：Sparse Hypergraphs:from Theory to Applications
报 告 人：葛根年 教授
报告时间：2025年5月10日 14：40
报告地点：文理楼290会议室
报告摘要：For fixed integersr, 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 introducedby Brown, , and in the 1970s. Since then, determining the upperand 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 sparsehypergraphs.
In this talk, we will introduce the recent developments on an important conjecture of Brown, , and on sparse hypergraphs, and discuss some unexpected applications of sparse hypergraphs to various topics in modern information sciences, including perfect and separatinghash families (data security), and centralized coded caching schemes (data transmission).
报告人简介：葛根年，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、密码学与信息安全、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230余篇，并被SCI他引2800余次，其中：85篇发表在国际组合数学及信息学领域内《Journal of Combinatorial Theory, Series A》、《SIAM Journal on Discrete Mathematics》等顶尖刊物上。现任中国通信学会信息通信及安全数学理论委员会主任、中国工业与应用数学学会编码密码及相关组合理论专委会副主任。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”。目前受邀担任多个主流SCI期刊的编委。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。先后主持国家杰出青年基金、国家自然科学基金重点项目、国家重点研发计划课题、国家自然科学基金面上项目共8项。已培养博士17名，其中4人成长为国家“四青”人才。
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