报告人：刘丽 教授
报告题目：Lorentzian polynomials and log-concavity of the independence polynomials of graphs
报告时间：2026年5月14日（周四）上午11：00
报告地点：云龙校区6号楼304报告厅
主办单位：数学与统计学院、数学研究院、科学技术研究院
报告人简介：
刘丽，教授，博士生导师。霍英东青年教师奖获得者，山东省泰山学者青年专家。主要从事多项式零点分布、矩阵全正性和组合不等式的研究。在Advances in Applied Mathematics等数学期刊上发表论文20余篇，所取得的成果被算法分析之父D.E. Knuth（高德纳）写入其经典巨著《The Art of Computer Programming》Vol.4B等多部专著中。主持国家自然科学基金项目多项。
报告摘要：
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.