5 problems

Let $E_2$ denote the Adams $E_2$ page for the sphere, viewed with its algebraic structure, and let its differentials be regarded as derivations. Uniqueness conjecture. The space of…

Let $\ell_2^{S}(i)$ denote the size function for the stable $2$-local homotopy groups of spheres. Isaksen–Wang–Xu's conjecture. There exists a nonzero constant $C$ such that … This…

Let $\ell_2^{S}(q)$ denote the size function for the stable $2$-local homotopy groups of spheres. Burklund and Senger show that $\ell_2^{S}(q)=\exp(O(\log(q)^3))$. Burklund–Senger'…

Cohen's existence conjecture. The space $T^{2n+1}(2^r)$ exists if $r>1$.

Double-loop-space conjecture. $W_n$ is a double loop space.