报告题目1：Flip Graphs for Polynomial Multiplication

报告人：陈绍示研究员，中国科学院数学与系统科学研究院

报告时间：2025年8月23日（周六）15:00-17:00

报告地点：20-200

报告摘要：Flip graphs were recently introduced in order to discover new matrix multiplication methods for matrix sizes. The technique applies to other tensors as well. In this paper, we explore how it performs for polynomial multiplication. This is a joint work with Manuel Kauers.

报告人简介：陈绍示, 现为中国科学院数学与系统科学研究院研究员。主要研究符号计算、机器证明与组合理论。在数学期刊Foundations of Computational Mathematics, Algebra and Number Theory, Math. Zeit., Selecta Mathematica等发表论文40余篇。目前担任中国数学会计算机数学专业委员会主任与国际符号与代数计算年会(ISSAC)指导委员会委员。曾获得第二届“吴文俊计算机数学青年学者奖”(2019)，第46届国际符号与代数计算年会(ISSAC2021)“杰出论文奖”，与国际计算机代数应用大会(ACA2022)“青年学者奖”。

报告题目2：An  identity relating Catalan numbers to tangent numbers with arithmetic applications

报告人：林志聪教授，山东大学

报告时间：2025年8月23日（周六）15:00-17:00

报告地点：20-200

报告摘要：We prove a combinatorial  identity relating Catalan numbers to tangent numbers arising from the study of peak algebra that was conjectured by Aliniaeifard and Li. This identity leads to the discovery of the intriguing identity $\sum_{k=0}^{n-1}{2n\choose2k+1}2^{2n-2k}(-1)^{k}E_{2k+1}=2^{2n+1},$ where $E_{2k+1}$ denote the tangent numbers. Interestingly, the latter identity can be applied to prove that $(n + 1)E_{2n+1}$ is divisible by $2^{2n}$ and the quotient is an odd number, a fact whose traditional proofs require significant calculations. Moreover, we find a natural $q$-analog of the latter identity with a combinatorial proof. This $q$-identity can be applied to prove Foata's divisibility property  of the  $q$-tangent numbers, which responds  to a problem raised by Sch\utzenberger.

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。