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Thursday, October 10, 2013

**Abstract:** Beginning with work of Farkas and Kra, a large number of partition identities have been established from theta function identities and modular equations in the past dozen years. In this lecture we examine a particular type of modular equation, namely, formulas for multipliers, and derive several interesting identities for colored partitions. We also examine 30 conjectured partition identities by Sandon and Zanello. We show that modular equations can be employed to prove many of these conjectures. This is joint work with Rui Zhou, who was a visiting graduate student from Dalian University during the past year. A review of the speaker's first lecture on this topic will be given.