报告题目 (Title)：关于广义秩为3的Nahm和的Mizuno猜想
报告人 (Speaker)：王博学（武汉大学）
报告时间（Time）：2025年6月8日（周日） 10：30
报告地点 (Place)：校本部GJ303
邀请人(Inviter)：陈旦旦
主办部门：理学院数学系
报告摘要：Mizuno providied 15 examples of generalized rank three Nahm sums with symmetrizer $\mathrm{diag}(1,2,2)$ 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 $\mathrm{diag}(1,1,2)$ and $\mathrm{diag}(1,2,2)$.
