3 problems

For the local $\mathbb{P}^2$, let $\widetilde{n}_d^{i,j}$ denote the combinatorial refined BPS invariants obtained from the Nekrasov partition function, and let $n_d^{i,j}$ denote…

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 $u=q^{2\sigma}$ and let $\tau$ and $\uptau$ denote the $c=1$ and $c=-2$ Painlevé VI tau functions, respectively. Let $\td{u}=\td{u}(u)$ and $\td{s}=\td{s}(s,\sigma)$ be functio…