11 problems

Extension and fixed-point formula conjecture. (1) The class $\mu(C)$ extends to a class in

Local structure conjecture. (1) There exists a proper continuous map

Let $X$ be a $4$-dimensional real manifold. Let $\mathcal{M}_k$ be the moduli space of $SU(2)$ instantons on $X$ of charge $k$, let $P_k$ be a principal bundle with $c_2(P_k)=k$, l…

Let $G$ be a simply-laced group, let $\mathcal{M}_{G,n}^\text{inst}$ denote the instanton moduli space with instanton number $n$, and define … Here $H_G^*$ denotes equivariant coho…

Let $L=\mathbb{C}^n$ and let $\tau=s_{\lambda}(x_1,\cdots,x_n)$ be the Schur polynomial associated with a partition $\lambda=(\lambda_1\geq\lambda_2\geq\cdots\geq\lambda_k)$. Let…

Let $\mathcal I_{\mathbb R^4}$ be the moduli space of instantons on $\mathbb R^4$, and let $\mathcal I_{\mathrm{TN}}$ be the moduli space of instantons on a Taub–NUT space. Instant…

Let $\mathcal M_C$ be the Coulomb branch of a framed affine quiver gauge theory. Affine instanton conjecture. Coulomb branches of framed affine quiver gauge theories are Uhlenbeck…

Conjectural generating-function claim. For $p>1$, $\widetilde{{\cal Z}}_N^{\, {\rm BH}}(\phi_0,\phi_2,y;p)$ is the corresponding generating function for the $\chi_y$-genus of the i…

Let $G$ be a group and let $\mathbb R^4/\mathbb Z_k$ be the corresponding orbifold. Consider the moduli space of $G$-instantons on this space and its intersection cohomology. Let t…

Let $G$ be a gauge group of ADE type, and consider the moduli space of $SU(N)$-instantons on a resolved ALE space of ADE type, together with its equivariant cohomology. Let the ass…

Connectedness conjecture. The full moduli space of unital-energy, rapidly decaying anti-instantons with trivial holonomy at infinity is obtained by the construction in this paper;…