报告人：王六权（武汉大学）

邀请人：张庆

报告时间：2023年9月21日（星期四）15:30-16:30

报告地点：东三十二楼216室

报告题目：Proofs of Zagier’s rank two examples for Nahm’s conjecture

报告摘要：Let $r\geq 1$ be a positive integer, $A$ a real positive definite symmetric $r\times r$ matrix, $B$ a vector of length $r$, and $C$ a scalar. Nahm's problem is to describe all such $A,B$ and $C$ with rational entries for which a specific $r$-fold $q$-hypergeometric series (denoted by $f_{A,B,C}(q)$) involving the parameters $A,B,C$ is a modular form. When the rank $r=2$, Zagier provided eleven sets of examples of $(A,B,C)$ for which $f_{A,B,C}(q)$ is likely to be a modular form. We present a number of Rogers-Ramanujan type identities involving double sums, which give modular form representations for Zagier's rank two examples. Together with several known cases in the literature, we verified all of Zagier's examples. In particular, we give the first $q$-series proof for the tenth example, whose explicit form was conjectured by Vlasenko and Zwegers in 2011. Part of this talk is based on a joint work with Zhineng Cao and Hjalmar Rosengren.

报告人简介：王六权，2014年本科毕业于浙江大学，2017年博士毕业于新加坡国立大学，现为武汉大学教授。他主要从事数论与组合数学领域的研究，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》、《Advances in Applied Mathematics》、《Journal of Number Theory》、《Ramanujan Journal》等期刊上发表学术论文40多篇，先后主持国家自然科学基金青年基金和面上项目各一项。