8 problems

Let $(u,A)^T$ be an entire critical point on $bbmathbb{R}^{n+2}$ satisfying … Write each $x \in \mathbb{R}^{n+2}$ as $x=(y,z) \in \mathbb{R}^2 \times \mathbb{R}^n$, and suppose als…

Let $M$ be a closed oriented Riemannian manifold with a non-zero relevant topological invariant, and let $D=\{(x_+,+1),(x_-,-1)\}$ consist of two oppositely labelled points at geod…

Let $(M,g)$ be a closed Riemannian manifold with $n=\dim M$, let $\xi^*\in H^1(M,\mathbb{Z}_2)$ be a flat bundle class selected by the variational principle, and let…

Inclusion conjecture.

In a Calabi–Yau $3$-fold or a $G_2$-manifold, generalized monopoles are critical points of the Yang–Mills–Higgs energy … The relevant invariants are expected to count generalized m…

Let $\mathfrak{O}$ be the state space and consider the Markov process on $\mathfrak{O}$ constructed in the paper for the stochastic Yang–Mills–Higgs equation on the three-dimension…

Codimension-two Yang–Mills–Higgs min-max equality conjecture. The estimate in the min-max comparison should hold with equality:

Montonen–Olive conjecture. In the simplest version, a sector with label $(m,n)$ should be equivalent, in a suitable sense, to the sector with label $(n,-m)$, with electric and magn…