图论与组合系列学术报告第6期——Clique density vs blowups

报告题目：Clique density vs blowups 报告人：刘鸿 首席科学家（韩国基础科学研究院IBS） 报告时间：2024年11月20日（周三）下午14：00-15：00 主持人：甘璐伊宁 特聘研究员 报告地点：北京邮电大学沙河校区 理学楼304 摘要：A well-known theorem of Nikiforov asserts that any graph with a positive -density contains a logarithmic blowup of . We explore variants of Nikiforov's result and investigate when positive clique density condition implies the existence of a significantly larger blowup of a clique. Our results study such problems for families of ordered graphs with forbidden induced monotone path, obtaining optimal bounds. As corollaries, we strengthen a result of Pach and Tomon, and resolve a conjecture of Tomon in a strong form. To find a large blowup, we reduce the embedding problem to a certain Ramsey problem. For optimal lower bound constructions, we make use of concentration of measure and the isodiametric inequality on high dimensional spheres. 报告人简介： 刘鸿，现任韩国基础科学研究院 (IBS) 首席科学家，同时为其极值及概率组合研究组 (ECOPRO) 带头人。2015年于伊利诺伊大学厄本那-香槟分校 (UIUC) 取得博士学位。研究领域包括极值、概率组合、图论、离散几何、组合数论等。在J. Amer. Math. Soc., Forum Math. Pi, J. Euro. Math. Soc., Amer. J. Math., Proc. London Math. Soc. 及J. Combin. Theory Ser. B, Combinatorica等杂志发表论文50余篇。并先后获得英国利弗休姆奖学金、欧盟的玛丽-居里奖学金，英国研究与创新（UKRI）联盟授予未来领袖学者的殊荣。