Many critical points for discrete Riesz energy on ${\mathbb{T}}^2$

François Clément, Stefan Steinerberger

It is widely believed that the energy functional $E_p:({\mathbb{S}}^2{)}^n\to \mathbb{R}$ $$E_p=\sum _{\genfrac{}{}{0ex}{}{i,j=1}{i\ne j}}^n\frac{1}{\Vert x_i-x_j{\Vert }^p}$$ has a number of cr…