22 problems

Let ASDYM denote the anti-self-dual Yang–Mills equations, and let an integrable model mean a model obtained through the dimensional-reduction construction under discussion. Ward's…

Let $K$ be the compact gauge quotient group, let $\rho_s$ be the heat-kernel measure on $K$ at time $s$, and let $P_s$ be the regularized measure on the space of connections…

Consider noncommutative extensions of integrable equations and noncommutative Lax equations arising in the study of reductions of noncommutative anti-self-dual Yang--Mills equation…

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

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…

Anti-self-dual Yang–Mills (ASDYM) equations form a class of exactly solvable nonlinear partial differential equations, and many two-dimensional Lax-integrable field equations arise…

In the Einstein–Yang–Mills system considered here, the intermediate regime exhibits episodes of approximate continuous self-similarity (CSS) within an overall discretely self-simil…

The paper considers … -ASD connections on general almost complex manifolds. This extends the uniqueness question beyond settings with isolated singularities or strong curvature bou…

Let corotational wave maps and equivariant Yang–Mills connections be considered in the settings described above, with the explicit self-similar blowup solutions and profiles introd…

Universal effective Lagrangian conjecture. The effective Lagrangian for all covariantly constant gauge fields has a universal form.

Uniqueness conjecture. The operator $\check C$ is unique.

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…

Consider a Yang–Mills amplitude represented in terms of color factors and kinematic numerators. The kinematic numerators are said to obey color-kinematics duality when they satisfy…

Let $G\subseteq U(N)$ be any compact non-Abelian Lie group for some $N\geq 2$, and consider any infinite-volume limit of four-dimensional lattice gauge theory with gauge group $G$…

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…

Let $\phi_0$ denote the self-similar blowup solution considered above, and consider generic blowup solutions in the corresponding equivariant wave-map or Yang–Mills model in dimens…

Large-$N$ spectral representation conjecture. The correlator should be a sum of an infinite number of free-field propagators,

Migdal's meromorphicity conjecture. The correlator is saturated by a sum of pure poles,

Scalar glueball pole-saturation conjecture. At next-to-leading order in $1/N$, the scalar glueball propagator is a sum of pure poles:

Large-$N$ pole-saturation conjecture. At next-to-leading order in $1/N$, the correlator is an infinite sum of free-field propagators,

Finite-time singularity conjecture. The solution goes singular in finite time, converging to a round point with $F\equiv 0$.

Small-data tail conjecture. For any given smooth compactly supported functions $\alpha(r)$ and $\beta(r)$, one can choose $\varepsilon$ such that, for each fixed $r>0$ and…