報(bào) 告 人：韓杰 教授
報(bào)告題目：Dense uniform hypergraphs have zero or many perfect matchings
報(bào)告時(shí)間：2025年02月24日（周一）下午3：00
報(bào)告地點(diǎn)：靜遠(yuǎn)樓1508會(huì)議室
主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院
報(bào)告人簡(jiǎn)介：
韓杰，北京理工大學(xué)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院教授，博導(dǎo)。研究圖論與組合數(shù)學(xué)及計(jì)算機(jī)理論，超圖中的子圖問(wèn)題。2015 年于美國(guó)佐治亞州立大學(xué)獲博士學(xué)位，2018 年-2020 年于美國(guó)羅德島大學(xué)任 tenure-track 助理教授，獲美Simons Foundation 基金資助（2019-2024）。2021 年獲國(guó)家高層次青年人才計(jì)劃，加入北京理工大學(xué)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院。在 Transactions of the American Mathematical Society 等雜志發(fā)表學(xué)術(shù)論文 60 余篇。
報(bào)告摘要：
Recently there has been exciting developments on the robust version of graph theory theorems. For hypergraph perfect matchings, it is shown by Pham-Sah-Sawhney-Simkin and Kang-Kelly-Kuhn-Osthus-Pfenninger that sufficiently large n-vertex k-uniform hypergraph with minimum codegree at least n 2 ? have many perfect matchings. We present a refinement of this result in the following sense: sufficiently large n -vertex k -uniform hypergraph with minimum codegree siginificantly larger than n k ? either has no perfect matching or many perfect matchings。