5 problems

The magma operad is an operad whose operations encode binary compositions, and $G=\operatorname{Gal}(\overline{\bold{Q}}/\bold{Q})$ acts on the genus-zero modular operad and its as…

Let $\overline{\mathcal{M}}_{*,*}$ be Getzler--Kapranov's modular operad, and let its profinite completion be equipped with its homotopy automorphism group. Let $\Lambda$ be the su…

Generation conjecture. The class generating $H_0(\Gamma_{0,3})$, together with the classes in the virtual cohomological dimension, generates all classes under the modular operad st…

Modular-operad isomorphism conjecture. There is a modular operad isomorphism

Let $\mathcal{QO}$ be the modular operad of surfaces of arbitrary genus with arbitrary numbers of boundary components and open ends, and let $\mathcal{A}\mathit{ss}$ be the cyclic…