7 problems

Kapustin–Witten counting conjecture. For each relative Chern number $m$, the number of solutions to the Kapustin–Witten equations with these boundary conditions equals the…

P=W conjecture. The two filtrations on the cohomologies of the moduli spaces coincide.

Witten's categorification conjecture. The moduli space $\mathfrak{M}_K^{\mathbb{R}^3}$ is related to the categorification of the Jones polynomial, namely Khovanov homology.

Let $X$ be a compact oriented Riemannian four-manifold with boundary, let $W=\partial X$ carry a knot or link $K$, and let $(A,\phi)$ solve the Kapustin–Witten equations with gener…

Hyperbolic flow inequality conjecture. For every $y>0$, one has

Let $W$ be a complete hyperbolic three-manifold. Consider the Kapustin–Witten equations for gauge group $SO(3)$ and parameter $t=-1$ on $W\times\mathbb{R}^+_y$, with Nahm pole boun…

Let $k$ be an integer, and consider the $5|k|$-dimensional family of singular solutions to the Kapustin–Witten equations on Euclidean $\mathbb{R}^4$ obtained by the generalized ADH…