6 problems

Let $q$-conformal blocks be the blocks associated with the $q$-difference isomonodromic deformation problem for $q$-Painlevé VI, and let their Fourier transforms define tau functio…

Let $\mathcal{Z}_{\mathrm{inst}}(i,i,i,iq^{\pm1/2},u;q^{-1},q|z^{1/2})$ denote the five-dimensional Nekrasov instanton partition function with the displayed special values of $v_i$…

Let $\tau(\boldsymbol{\theta};\sigma,s|t)$ be the tau function defined from the five-dimensional Nekrasov partition function, and let…

Let $\mathcal{Z}_{tv}(\boldsymbol{\theta},\sigma|t)$ denote the normalized five-dimensional Nekrasov partition function with four matter fields appearing in the $q$-Painlevé VI tau…

The translations and transformations introduced earlier imply generalized $q$-Painlevé VI systems; in particular, the relevant translation $\mathcal{V}$ has a factor $\pi$. The q-G…

Let $q$-$P_{(n+1,n+1)}$ denote the system of $q$-difference equations introduced above, with parameters $t,q\in\mathbb{C}$ and $|q|<1$. Let Tsuda's higher-order $q$-Painlevé system…