講座名稱：Sparse Hypergraphs: from Theory to Applications

講座人：葛根年 教授

講座時(shí)間：8月30日10:00

講座地點(diǎn)：北校區(qū)新科技樓1012學(xué)術(shù)報(bào)告廳

講座人介紹：

葛根年，首都師范大學(xué)特聘教授。長期從事組合數(shù)學(xué)、編碼理論、信息安全、壓縮感知、數(shù)據(jù)科學(xué)等數(shù)學(xué)與信息交叉科學(xué)研究。迄今共發(fā)表SCI論文200余篇，并被SCI他引1900余次，其中：65篇發(fā)表在國際組合數(shù)學(xué)及信息學(xué)領(lǐng)域內(nèi)頂尖刊物 《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年愛思唯爾（Elsevier）發(fā)布“中國高被引學(xué)者（Most Cited Chinese Researchers）”榜單以來，一直進(jìn)入榜單。同時(shí)，入選美國斯坦福大學(xué)發(fā)布的“2020全球前2%頂尖科學(xué)家（World's Top 2% Scientists 2020）”榜單、美國數(shù)學(xué)會(huì)發(fā)布的“高被引數(shù)學(xué)家（Most cited mathematicians）”榜單?，F(xiàn)任中國數(shù)學(xué)會(huì)組合數(shù)學(xué)與圖論專業(yè)委員會(huì)主任、國際組合數(shù)學(xué)及其應(yīng)用協(xié)會(huì)“Medals Committee Member”（全球共3人）。目前受邀擔(dān)任國際組合數(shù)學(xué)界頂尖SCI期刊《Journal of Combinatorial Theory, Series A》、國際信息理論界頂尖SCI期刊《IEEE Transactions on Information Theory》、國際編碼密碼界權(quán)威SCI期刊《Designs, Codes and Cryptography》、國際組合設(shè)計(jì)界權(quán)威SCI期刊《Journal of Combinatorial Designs》、國際代數(shù)組合界權(quán)威SCI期刊《Journal of Algebraic Combinatorics》、國內(nèi)權(quán)威SCI期刊《中國科學(xué)：數(shù)學(xué)》、國內(nèi)SCI期刊《高校應(yīng)用數(shù)學(xué)學(xué)報(bào)》的編委。曾獲國際組合數(shù)學(xué)及其應(yīng)用協(xié)會(huì)頒發(fā)的“Hall Medal”、中國青年科技獎(jiǎng)、教育部自然科學(xué)二等獎(jiǎng)、浙江省科學(xué)技術(shù)二等獎(jiǎng)。

講座內(nèi)容：

More than forty years ago, Brown etc. 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. Together with Alon and Shapira, they posed a well-known conjecture, which 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 fixed integers r ≥ k + 1 ≥ e ≥ 3. And we use tools from additive combinatorics to show 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 of Walker and Colbourn on perfect hash families. This conjecture had been open for ten years and traditional methods seem to have limited effect on it. We also use the (6,3)-free hypergraphs to construct two classes of placement delivery ar- rays which are useful for centralized coded caching. The complexity of the PDAs is reduced from exponential to sub-exponential.

主辦單位：通信工程學(xué)院