6 problems

Let $\alpha\in H_{n-1}(\mathbb{T}^n,\mathbb{R})$ be a totally irrational class. For rational classes $r_k$ converging to $\alpha$, let $\Delta W_{r_k}=\omega(r_k)-S(r_k)$. Continui…

Let $g$ be a Riemannian metric on $\mathbb{T}^n$. Suppose that the min-max barriers vanish simultaneously in every primitive homology class, so that there is a foliation of…

Relative spectrum conjecture.

Nine-distance conjecture. For every $N\in{\mathbb N}$,

Let ${{\mathcal P}_{n}}\subset [0,1]^2$ be a point set with $n$ points, and let $\operatorname{disp}({{\mathcal P}_{n}})$ denote the area of the largest rectangle in the two-dimens…

Let $R$ and $r$ be the major and minor radii of the torus, and set $\mu=R/r$. Let $\alpha_p\equiv\pi/2$ denote the constant critical configuration, and let the nonconstant equilibr…