7 problems

Let $X$ be a rational surface, let $v_0$ denote the relevant charge, let $Z_{v_0}(\tau)$ be its partition function, let $\widetilde{Z}_{v_0}^{int}(\tau)$ be the corresponding integ…

Let $G$ be a group with associated affine Lie algebra $\widehat{g}$, let $\Gamma=\mathbb{Z}_k$ be a cyclic group, and consider the moduli space of $G$-instantons on the resolution…

Let $M$ be the moduli space of instantons, let $S(TM)$ denote its chiral spin bundle, and let ${\cal L}^{(I)}$ be a line-bundle object over $M$ for which only…

Let $\mathcal{M}_{SU(k)}^N(\mathbb{R}^4)$ denote the moduli space of $SU(k)$ $N$-instantons on $\mathbb{R}^4$. Consider the $\mathcal{N}=(4,4)$ supersymmetric sigma model with this…

Let $G=SL(2)$, with four fundamental matters and adjoint matters, and let the corresponding instanton partition functions be defined by equivariant integration over the relevant in…

Braverman's Uhlenbeck compactification conjecture. The convolution diagram for the double affine Grassmannian realizing the tensor product should be defined by the Uhlenbeck partia…

Braverman–Finkelberg's geometric Satake conjecture. Intersection cohomology sheaves on the Uhlenbeck compactification of the framed moduli space of $G_{\mathrm{cpt}}$-instantons on…