(-2) blow-up formula

Abstract: We prove functional equations of Nekrasov partition functions for $A_{1}$-singularity, suggested by Ito-Maruyoshi-Okuda. Furthermore, we want to propose (-2) blow-up formula. We consider the minimal resolution of $A_{1}$ singularity, the quotient stack of the plane by $\lbrace \pm 1 \rbrace$, and moduli spaces of framed sheaves on them. Our formulas relate integrals over these moduli spaces for some cases. Our proof is given by the method by Nakajima-Yoshioka based on the theory of wall-crossing formula developed by Mochizuki. The presentation will be in Japanese (slides will be in English).

JapaneseMathematics

Audience: researchers in the discipline

Comments: The password of this zoom talk will be provided shortly before the talk in the colloquium web page so-okada.github.io/nitoc-math-colloquium.html

Math Colloquium at NITOC