Joint seminar on Mathematical Physics of NRU HSE and Skoltech Center for Advanced Studies : Anton Shchechkin (Skoltech, HSE)

Gamayun, Iorgov and Lisovyy in 2012 proposed that tau function of the Painlevé equation equals to the series of с=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 blow-up relations on Nekrasov partition functions. 

We also study series of q-deformed c=-2 conformal blocks and relate it to q-Painlevé equation.
Using this we prove formula for the tau function of q-Painleve  A_7^{(1)'}  equation (based on arXiv:1811.04050v1)