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The goal of this note is to study integrable properties of a generating function of the HOMFLY-PT invariants of the Hopf link colored with different representations. We demonstrate that such a generating function is a τ-function of the KP hierarchy. Furthermore, this Hopf generating function in the case of composite representations, which is a generating function of the 4-point functions in topological string (corresponding to the resolved conifold with branes on the four external legs), is a τ-function of the universal character (UC) hierarchy put on the topological locus. We also briefly discuss a simple matrix model associated with the UC hierarchy.

While the field of economics lacks diversity, there is little consensus on the underlying causes of or most effective solutions to this problem. The authors of this article combine data from the Integrated Postsecondary Education Data System (IPEDS) with data from their own survey of U.S. economics departments to identify institution and department characteristics associated with observed variation in gender and racial diversity of undergraduate students across departments. They focus their attention on student support, role modeling, course content, and the use of active learning pedagogy. While they find no significant associations between course content or student support with student diversity, they find that gender diversity in departmental faculty is a strong predictor and that active learning is positively associated with gender diversity. [ABSTRACT FROM AUTHOR]