报告名称：Proofs of Mizuno’s conjectures on rank two Nahm sums

报告专家：王六权

专家所在单位：武汉大学

报告时间：2023年11月30日16:00

报告地点:数统学院201

专家简介：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。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。

报告摘要：Recently, Mizuno studied Nahm sums associated with symmetrizable matrices. He provided 14 sets of candidates of modular Nahm sums in rank two and justified four of them. We prove the modularity for eight other sets of candidates and present conjectural formulas for the remaining two sets of candidates. This is achieved by finding Rogers-Ramanujan type identities associated with these Nahm sums. We also prove Mizuno's conjectural modular transformation formula for a vector-valued function consists of Nahm sums. Meanwhile, we find some new non-modular identities for some other Nahm sums associated with the matrices in Mizuno's candidates. This talk is based on a joint work with Boxue Wang.