报告题目1：Coefficientwise total positivity and Stieltjes moment properties from Riordan arrays

报告人：祝宝宣教授，江苏师范大学

报告时间：2025年11月26日（周三）9:30-12:00

报告地点：腾讯会议：402 759 342

报告摘要：Total positivity of matrices plays an important role in various branches of mathematics.  In this talk, we present some criteria for the coefficientwise total positivity and the coefficientwise Hankel-total positivity from Riordan arrays. We will apply our results to a few well-known combinatorial triangles in a unifed approach.

报告人简介：祝宝宣，博士、教授、博士生导师，入选国家级青年高层次人才、江苏省青年高层次人才，及江苏省“333高层次人才工程”中青年领军人才计划。主要研究方向为解析组合学，已在《Memoirs of AMS》、《Adv. Math.》、《J. Combin. Theory Ser. A》等数学期刊上发表SCI论文50余篇；先后主持国家自然科学基金项目5项、科技部重点研发项目课题1项。曾受邀在世界华人数学家大会、德国“黑森林数学研究所”研讨会、中国数学会学术年会、中国运筹学会学术年会、全国组合数学图论大会等会议上作报告，获得江苏省青年科技奖、江苏省数学成就奖等奖项。

报告题目2：Total positivity of the matrix related to j-Eulerian numbers

报告人：牟丽丽副教授，江苏师范大学

报告时间：2025年11月26日（周三） 9:30-12:00

报告地点：腾讯会议：402 759 342

报告摘要：Define the numbers of permutations of $[n]$ which have $i$ descents and begin with $j$ to be $$A(n,i,j)=|\{\pi\in S_n:\des(\pi)=i,\ \pi(1)=j\}|.$$ Let $H_n=[h_{i,j}]_{i,j=1}^{n}$ be the $n\times n$ matrix with entries $h_{i,j}=A(n,i-1,j)$. The matrix $H_n$ is defined in geometric combinatorics as the transformation matrix for the $h$-vector under barycentric subdivision. Mu and Welker proved that this matrix is TP$_2$ (i.e., all its $2$-minors are nonnegative) and conjectured that it is, in fact, totally positive (TP). The main objective of this paper is to prove this conjecture.

报告人简介：牟丽丽，江苏师范大学数学与统计学院副教授，研究领域为组合数学。大连理工大学-麻省理工学院联合培养博士，伦敦大学学院、麻省理工学院、德国马尔堡大学等机构访问学者。主持国家自然科学基金项目2项。现任中国工业与应用数学学会-图论组合及应用专委会委员。

报告题目3：q-Supercongruences for truncated q-Appell series

报告人：王晓霞教授，上海大学

报告时间：2025年12月1日（周一） 16:00-18:00

报告地点：腾讯会议：507 952 698

报告摘要：Congruences and q-congruences for the truncated Appell series are quite finite in the literature. In this paper, we introduce the truncated q-Appell series and investigate their congruence properties.

Specifically, using two hypergeometric summations, the `creative microscoping' method formulated by Guo and Zudilin and the Chinese remainder theorem for coprime polynomials, we establish some q-supercongruences on the truncated q-Appell series $\Phi^{(1)}, \Phi^{(2)}, \Phi^{(3)}$. Moreover, in terms of the q-Zeilberger algorithm, a q-supercongruence for the truncated q-Appell series $\Phi^{(4)}$ is built, which is a new q-analogue of a conjecture of Apagodu and Zeilberger. As conclusions, we immediately obtain some congruences of the truncated Appell series.

报告人简介： 王晓霞，博士，上海大学教授。主要研究领域为组合数学和特殊函数，主要研究方向包括组合恒等式、q-级数恒等式、q-级数同余式等。截至目前，已在《Adv. Appl. Math.》、《Proc. Amer. Math. Soc.》、《Forum. Math.》等国际高水平杂志上发表SCI论文60余篇，主持国家自然科学基金项目2项、上海市自然科学基金2项。

邀请人：离散数学研究所