We investigate partition functions defined from integrals over the handsaw quiver varieties of type $A_{1}$ via wall-crossing phenomena. We consider vortex partition functions defined by two types of cohomology classes, and get functional equations for each of them. This gives proofs to formulas suggested by physical computations. In particular, we obtain geometric interpretation of formulas for multiple hypergeometric functions including rational limit of the Kajihara transformations formula. We also introduce analogous computations for integrals over Grassmannian manifolds, and more general settings for framed quiver representations.

This seminar is a hybrid meeting:
Meeting ID：880 8640 6545 Passcode: 225908