报告主题：Clique density vs blowups

报 告 人：刘鸿 教授

报告时间：2024年10月25日（周五）上午9：30-10：30

报告地点：腾讯会议 （会议号:865-764-175）

报告摘要: A well-known theorem of Nikiforov asserts that any graph with a positive Kr-density contains a logarithmic blowup of Kr. 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，2015年在伊利诺伊大学厄本那-香槟分校（UIUC）取得博士学位，师从József Balogh。2016年在华威大学数学研究所做博士后研究员。后于2019年在华威大学（Warwick）取得终身教职，并摘获英国科研创新未来领袖奖。于2022年加入韩国基础科学研究院（IBS）任首席科学家，现是其极值及概率组合研究组（ECOPRO）的领头人, SIAM Journal on Discrete Mathematics杂志的编委，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 of Mathematics, Pi，American J. Mathematics，J. Euro. Math. Soc.，Proc. London Math. Soc.，J. London Math. Soc.，Proc. Amer. Math. Soc.，Forum of Mathematics, Sigma，J. Combin. Theory Ser. B，J. Combin. Theory Ser. A及Combinatorica等顶级杂志发表多篇学术论文，并多次受邀在国际学术会议上做邀请报告。