报告题目1：Lorentzian polynomials and log-concavity of the independence polynomials of graphs

报告人：刘丽教授，曲阜师范大学

报告时间：2026年3月8日（周日）9:00-12:00

报告地点：20-306

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 Erdos, but also unify many known results.

报告人简介：刘丽，曲阜师范大学教授，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，山东省“组合数学及其应用”创新团队带头人。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AAM, JAC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。作为第一完成人荣获山东省自然科学三等奖和山东省高等学校科学技术奖一等奖各1项。

报告题目2：Product version of Hilton-Milner Theorem on cross-intersecting families

报告人：张华军教授，绍兴大学

报告时间：2026年3月8日（周日）9:00-12:00

报告地点：20-308

报告摘要：A family $\mathcal A$ is said to be nontrivial if $\cap_{A\in\mathcal A}A=\emptyset$. Two families $\mathcal A$ and $\mathcal B$ are called cross-$t$-intersecting if $|A\cap B|\geq t$ for all $A\in\mathcal A$ and $B\in \mathcal B$.  In this talk, we will introduce some results on the cross-intersecting families and prove the following result: If $\mathcal A$ and $\mathcal B$ are nontrivial cross-intersecting families of $\binom{[n]}{k}$, then \[|\mathcal A||\mathcal B|\leq\left(\binom{n-1}{k-1}-\binom{n-k-1}{k-1}+1\right)^2.\]

报告人简介：张华军，绍兴大学教授，浙江省高校中青年学科带头人，中国组合数学与图论专业委员会委员。2007年1月毕业于大连理工大学并获博士学位，主要从事组合极值理论研究，解决了该领域中的一些公开问题和猜想，在J. Combin.Theory Ser. A、J. Combin.Theory Ser. B、J.Graph Theory和SIAM J. Discrete Math.等期刊上发表论文20余篇，主持或参与完成多项国家自然科学基金。

报告题目3：Web permutations, Seidel triangle and normalized $\gamma$-coefficients

报告人：林志聪教授，山东大学

报告时间：2026年3月8日（周日）14:00-17:00

报告地点：20-306

报告摘要：The web permutations were introduced by Hwang, Jang and Oh to interpret the entries of the transition matrix between the Specht and $\mathrm{SL}_2$-web bases of the irreducible $\S_{2n}$-representation indexed by $(n,n)$. They conjectured that certain classes of web permutations are enumerated by the Seidel triangle. Using generating functions, Xu and Zeng showed that enumerating web permutations by the number of drops, fixed points and cycles gives rise to the normalized $\gamma$-coefficients of the $(\alpha,t)$-Eulerian polynomials. They posed the problems to prove their result combinatorially and to find an interpretation of the normalized $\gamma$-coefficients in terms of cycle-up-down permutations. In this work, we prove the enumerative conjecture of Hwang-Jang-Oh and answer the two open problems proposed by Xu and Zeng. This talk is based on joint work with Yao Dong and Qiongqiong Pan.

报告人简介：林志聪，山东大学数学与交叉科学研究中心教授，国家青年高层次人才。主要从事计数组合学的研究，在J. Combin. Theory Ser. A、Combinatorica等权威期刊发表SCI学术论文40余篇。任中国数学会计算机数学专业委员会委员和中国运筹学会图论组合分会青年理事。

邀请人：离散数学研究所