6 problems

Penrose's conjecture. A quasi-local description of conserved quantities should exist, at least for energy-momentum and angular momentum.

Let $M(\theta,\phi)$ be the two-parameter family of integrals of motion obtained by multiplying the local tensors described above, with $(\theta,\phi)$ parametrizing the spherical…

A quantum spin system is integrable when it possesses local conserved quantities. In a one-dimensional system with translational symmetry and nearest-neighbor interactions, a conse…

Let $G$ be an affine-affine $ADE$ bigraph in the classification, and let $A(t)$ be a function of the system parameters at time $t$. It is a time-dependent conserved quantity if the…

Simultaneous-rotation conjecture. Only simultaneous rotations of $6k$, with $k\in\mathbb{Z}$, are able to achieve this condition.

Extremal rotation conjecture. Any rotation that transforms an extremum to another extremum of the same braid must take the form