Painlevé equations from Nakajima-Yoshioka blowup relations

Gamayun, Iorgov and Lisovyy in 2012 proposed that tau function of the Painlevé equation is equal to the series of c=1 Virasoro conformal blocks. We study similar series of c=-2 conformal blocks and relate it to Painlevé theory. The arguments are based on Nakajima-Yoshioka blowup relations on Nekrasov partition functions. We also study series of q-deformed c=-2 conformal blocks and relate it to q-Painlevé equation. As an application, we prove formula for the tau function of q-Painlevé A_7^{(1)'} equation.