6 problems

Let $\mathcal{E}$ be the energy functional for spherical ferromagnets, and let a saddle point of first type denote one of the axisymmetric critical points with mapping degree zero…

Let $\mathcal{E}$ be the energy functional for spherical ferromagnets, and let $\kappa_0\geq 4$ be such that for every $\kappa>\kappa_0$ there exists a first-type saddle point of…

Positivity conjecture. This sum is positive for any choice of $y_i\in\mathbb{R}^3\setminus\{a_i\}$.

Uniqueness conjecture. Solutions to in $\mathcal M$ satisfying the displayed pointwise bound are unique.

Let Skyrmions be topologically protected quasiparticles in a two-dimensional spin lattice, and consider their behavior in the presence of dipolar interactions. Dipole-interaction r…

Consider configurations in quantum chromodynamics carrying multiple Skyrmion charges. Hidden torus-knot structure conjecture. A hidden torus-knot structure can be expected in such…