I will follow up on my related colloquium talk, where I will introduce the basic questions and topics on Stanton's conjectures for ranks and cranks and new modular forms techniques for producing infinite families of crank-type functions "explaining" modular forms. There will be an emphasis on examples and context within modular forms, Jacobi forms, and the connections with sum=product formulas in combinatorics which arise from Lie theory. I will also go into more details of the proofs and further applications than in the colloquium. The talk will be for a general number theory audience, with no prior knowledge of modular forms required. Time permitting, I will give more details on the analytic ingredients including exact formulas for partition-type functions and how to apply them to give effective bounds on ranges for inequalities.