7 problems

Let $G$ be a gauge group with gauge coupling $\tau$, and let $G^\vee$ be a group whose Lie algebra satisfies $\operatorname{Lie}(G^\vee)=\mathfrak{g}=\operatorname{Lie}(G)$. Let…

Soliton resolution conjecture. Any smooth, finite-energy solution $W(t,r)$ tends as $t\to\infty$, modulo sign, either to the half-kink or to a rescaled half-kink together with an a…

Let $\mathcal G$ be a compact Lie group with Lie algebra $\mathbf g$, let $s_0=\frac{n-2}{2}$ be the scaling index, and consider the Yang–Mills equation … for a connection with cur…

Let $G_N$ be a classical compact matrix Lie group of size $N$, and let $\Sigma$ be a compact surface, the Euclidean plane $\mathbb{R}^2$, or the Poincare9 disc…

Bubbling for Yang–Mills. Either $T_{+}=\infty$, or there are such sequences for which $A_{(n)}$ converges, through its curvature, to a Lorentz transform of a nontrivial finite-ener…

Odd-dimensional all-time existence conjecture. The solution to the Ricci Yang-Mills flow exists for all time.

All-time existence conjecture. The solution to the Ricci Yang-Mills flow with initial condition $(g,A)$ exists for all time.