Proofs of Mizuno＇s Conjectures on Generalized Rank Three Nahm Sums

主讲人：王博学 武汉大学

时间：2025年6月7日13：00

地点：徐汇校区三号楼332室 

举办单位：数理学院

主讲人介绍：王博学，武汉大学博士生，师从王六权教授，并入选武汉大学数学学院拔尖人才培养计划。其主要研究领域为q-级数与模形式，特别在Rogers-Ramanujan型恒等式的研究中取得一定进展，其研究成果已发表于《Advances in Mathematics》，《Transactions of the American Mathematical Society》等期刊。

内容介绍：Mizuno providied 15 examples of generalized rank three Nahm sums with symmetrizer diag(1,2,2) which are conjecturally modular. Using the theory of Bailey pairs and some q-series techniques, we establish a number of triple sum Rogers--Ramanujan type identities. These identities confirm the modularity of all of Mizuno＇s examples except for two non-modular cases. We show that the two exceptional cases of Nahm sums are sums of modular forms of weights 0 and 1. We also prove Mizuno＇s conjectural modular transformation formulas for two vector-valued functions consisting of Nahm sums with symmetrizers diag(1,1,2) and diag(1,2,2).