数学学科Seminar第2271讲

创建时间:  2025/05/30  邵奋芬   浏览次数:   返回

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):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 $\mathrm{diag}(1,2,2)$.



下一条:数学学科Seminar第2851讲 裂隙介质核素迁移分数阶导数升尺度建模及应用


数学学科Seminar第2271讲

创建时间:  2025/05/30  邵奋芬   浏览次数:   返回

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):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 $\mathrm{diag}(1,2,2)$.



下一条:数学学科Seminar第2851讲 裂隙介质核素迁移分数阶导数升尺度建模及应用