10 problems

Let $X$ be a space and let $n$ be an integer. Consider fully extended, degree $-n$, 2-dimensional supersymmetric field theories over $X$, modulo concordance. Segal–Stolz–Teichner c…

Let $\mathrm{tmf}$ be the connective topological modular forms spectrum, let $\overline{\mathrm{tmf}}$ denote its cofiber in the unit decomposition, and let…

In the $\mathrm{tmf}$-Adams spectral sequence for $Z$, let $\epsilon_j,\bar\epsilon_j\in\{0,1\}$ and let $m\gg0$. Differentials conjecture, part 2. The $v_2$-families … support dif…

Let $x_i=h_{i,0}^2$ in the $\mathrm{tmf}$-Adams spectral sequence for $Z$. Hidden-extension conjecture. There are hidden extensions … This is suggested by comparing the known…

Let $x_j=h_{j,0}^2$. In the $\mathrm{tmf}$-Adams spectral sequence for $Z$, use indices $i\geq3$, $l\geq i+3$, $m<2^{i+1}-1$, $k_j\geq0$, and $\epsilon_j,\bar\epsilon_j\in\{0,1\}$.…

$\mathcal{E}_\infty$ 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

Epimorphism conjecture. A $2$-local characteristic morphism

Characteristic morphism conjecture. Each of the three displayed maps is a characteristic morphism.

Loop-space TMF to twisted K-theory conjecture. There is a map