報(bào)告題目：Clique density vs blowups
報(bào)告人：劉鴻 首席科學(xué)家（韓國(guó)基礎(chǔ)科學(xué)研究院IBS）
報(bào)告時(shí)間：2024年11月20日（周三）下午14：00-15：00
主持人：甘璐伊寧 特聘研究員
報(bào)告地點(diǎn)：北京郵電大學(xué)沙河校區(qū) 理學(xué)樓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.
報(bào)告人簡(jiǎn)介：
劉鴻，現(xiàn)任韓國(guó)基礎(chǔ)科學(xué)研究院 (IBS) 首席科學(xué)家，同時(shí)為其極值及概率組合研究組 (ECOPRO) 帶頭人。2015年于伊利諾伊大學(xué)厄本那-香檳分校 (UIUC) 取得博士學(xué)位。研究領(lǐng)域包括極值、概率組合、圖論、離散幾何、組合數(shù)論等。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等雜志發(fā)表論文50余篇。并先后獲得英國(guó)利弗休姆獎(jiǎng)學(xué)金、歐盟的瑪麗-居里獎(jiǎng)學(xué)金，英國(guó)研究與創(chuàng)新（UKRI）聯(lián)盟授予未來(lái)領(lǐng)袖學(xué)者的殊榮。
