报告题目1：Some extremal problems on color-critical graphs, and beyond

报告人：李书超教授，华中师范大学

报告时间：2025年10月29日（周三）10:00-12:00

报告地点：腾讯会议：475836299

报告摘要：Turán-type problem is a fundamental problem in extremal graph theory. The spectral Turán-type problem is a newly developed one in this field. Both of these two types of extremal problems attract more and more researchers’ attention. In this talk, we first introduce the background in this field. Then we present our results related to above two types of extremal problems on color-critical graphs. Finally, we propose some further research issues along this line.

报告人简介：李书超，华中师范大学数学与统计学学院教授，博士生导师。主要研究方向为极值图论与图谱理论，研究成果相继在Journal of Graph Theory、European Journal of Combinatorics、Advances in Applied Mathematics、Electronic Journal of Combinatorics、Discrete Mathematics等多个重要国际学术期刊发表SCI论文100余篇；主持国家自然科学基金项目5项；入选教育部“新世纪优秀人才支持计划”；主持完成的项目“图的几类不变量的研究”获湖北省自然科学奖三等奖。现担任中国运筹学会图论组合分会常务理事、中国工业与应用数学学会图论组合及其应用专委会常务委员。

报告题目2：Equivariant inverse Kazhdan--Lusztig polynomials of thagomizer matroids

报告人：郜璐璐副教授，西北工业大学

报告时间：2025年10月30日（周四）10:00-12:00

报告地点：腾讯会议：691869421

报告摘要：In this talk, we focus on the equivariant inverse Kazhdan--Lusztig polynomials of thagomizer matroids, a natural family of graphic matroids associated with the complete tripartite graphs $K_{1,1,n}$. These polynomials were introduced by Proudfoot as an extension of the Kazhdan--Lusztig theory for matroids. We derive closed-form expressions for the $S_n$-equivariant inverse Kazhdan--Lusztig polynomials of thagomizer matroids and present them explicitly in terms of the irreducible representations of $S_n$. As an application, we also provide explicit formulas for the non-equivariant inverse Kazhdan--Lusztig polynomials, originally defined by Gao and Xie, and give an alternative proof using generating functions.  Furthermore, we prove that the inverse Kazhdan--Lusztig polynomials of thagomizer matroids are log-concave.

报告人简介：郜璐璐，西北工业大学副教授。毕业于南开大学组合数学中心，师从杨立波教授。研究方向为代数组合学，主要包括拟阵多项式理论、对称函数理论等，在JCTB、Siam 离散、Proceedings AMS等期刊上发表科研论文多篇。

邀请人：严慧芳