报告题目1：Some New Modular Nahm Sums from a Lift-Dual Operation

报告人：王六权教授，武汉大学

报告时间：2025年11月5日（周三） 9:00

报告地点：腾讯会议：753127232

报告摘要：Around 2007, Zagier discovered some rank two and rank three Nahm sums, and their modularity have now all been confirmed. Zagier also observed that the dual of a modular Nahm sum is likely to be modular.  This duality observation motivates us to discover some new modular rank three and rank four Nahm sums by a lift-dual operation. We first lift Zagier's rank two Nahm sums to rank three and then calculate their dual, and we show that these dual Nahm sums are indeed modular. Applying the same operation to some modular rank three Nahm sums, we obtain some rank four Nahm sums and confirm their modularity. We achieve this by establishing the corresponding Rogers--Ramanujan type identities, which express these Nahm sums as modular infinite products. As a byproduct, we find new counterexamples to Zagier's duality observation. This talk is mainly based on joint works with Zhineng Cao.

报告人简介：王六权，武汉大学数学与统计学院教授，主要从事组合数学与数论领域的研究，研究课题多集中在q-级数、整数分拆、特殊函数、模形式理论等方面。迄今在《Advances in Mathematics》、《Transactions of the American Mathematical Society》、《Journal of Combinatorial Theory Series A》、《Advances in Applied Mathematics》、《Journal of Number Theory》等期刊上发表学术论文50多篇，先后主持国家自然科学基金青年基金、面上项目、国家重点研发计划青年科学家项目各一项。

报告题目2：The log-behavior in Hoggatt triangles

报告人：毛建玺副教授，大连理工大学

报告时间：2025年11月5日（周三）9:00

报告地点：腾讯会议：753127232

报告摘要：The d-Hoggatt triangle is a lower triangular matrix, whose entries are generated from specific minors of Pascal's triangle with consecutive d rows and d columns. Pascal's triangle, the Narayana triangle and the Baxter triangle correspond to the $d$-Hoggatt triangle for d=1,2 and 3, respectively. In this paper, we show that the sequences in the d-Hoggatt triangle share various log-concavity and log-convexity properties with those in Pascal's triangle. We present the infinite log-concavity of the row sequences and column sequences, the log-concavity of the sequences along the transversals, and asymptotic log-convexity of the sequences along the rays of the $d$-Hoggatt triangle. In addition, we prove the asymptotic normality of the row sequences and total positivity of the d-Hoggatt triangle.

报告人简介：毛建玺，1992年生，大连理工大学副教授。2021年毕业于大连理工大学，获理学博士学位，研究方向为组合数学。主要研究兴趣包括解析组合学和计数组合学。在组合数学领域主流期刊发表论文十余篇。主持国家自然科学基金青年项目，主持完成中国博士后面上基金项目。

邀请人：严慧芳