4 problems

Let $F$ be a space and let $R:= \operatorname{Thom}(\Omega F \to BO \times \mathbb{Z})$ be the associated unital ring spectrum. Let $\operatorname{Flow}^F$ denote the stable…

$\mathcal{E}_\infty$ Thom spectrum conjecture. There is an $\mathcal{E}_\infty$ morphism $Mj\to\mathrm{tmf}_1(3)$ which factors through $Mj/\!/w_4,w_8,w_{12}$, and the induced morp…

Epimorphism conjecture. The $\mathcal{E}_\infty$ orientation $Mj_3\to\mathrm{tmf}$ induces a ring epimorphism

Spectrum-level splitting conjecture. As a spectrum, $Mj_2$ is a wedge of $k\mathrm{O}$-module spectra, $Mj_3$ is a wedge of $\mathrm{tmf}$-module spectra and $Mj^{\mathrm{c}}$ is a…