報告人：劉麗 教授
報告題目：Lorentzian polynomials and log-concavity of the independence polynomials of graphs
報告時間：2026年5月14日（周四）上午11：00
報告地點：云龍校區6號樓304報告廳
主辦單位：數學與統計學院、數學研究院、科學技術研究院
報告人簡介：
劉麗，教授，博士生導師。霍英東青年教師獎獲得者，山東省泰山學者青年專家。主要從事多項式零點分布、矩陣全正性和組合不等式的研究。在Advances in Applied Mathematics等數學期刊上發表論文20余篇，所取得的成果被算法分析之父D.E. Knuth（高德納）寫入其經典巨著《The Art of Computer Programming》Vol.4B等多部專著中。主持國家自然科學基金項目多項。
報告摘要：
In this paper, we first construct two graphs F(l,m,t,s) and G_4(l,m,t,s). Then we obtain infinite graphs F_n(l,m,t,s) and the operator E_{G_4(l,m,t,s)},where F_n(l,m,t,s) is defined by glueing the vertex of n copies F(l,m,t,s), and E_{G_4(l,m,t,s)} is defined by replacing each edge of G with G_4(l,m,t,s), for any arbitrary simple undirected graph G. By using the theory of Lorentzian polynomial, we prove that the independence polynomials of graphs F_n(l,m,t,s) and the image graphs of E_{G_4(l,m,t,s)} are log-concave, respectively. As applications, our results not only make progress on the conjecture of Alavi, Malde, Schwenk and Erd\H{o}s, but also unify known results.