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## Painlevé equations from Nakajima–Yoshioka blowup relations

Letters in Mathematical Physics. 2019. Vol. 109. No. 11. P. 2359-2402.

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 $A^{(1)′}_7$ equation.