The Kawazumi–Morita invariant-cohomology conjecture for Torelli groups

Let $\mathcal{I}_g$ be the Torelli group of a closed genus-$g$ surface, and let $e_{2i}$ denote the Mumford–Morita–Miller class of degree $4i$. Kawazumi–Morita's conjecture. Stably, there is an isomorphism of graded algebras

$$H^*(\mathcal{I}_g,\mathbb{Q})^{\operatorname{Sp}(2g,\mathbb{Z})}\cong\mathbb{Q}[e_2,e_4,\ldots].$$

The source attributes this conjecture to Kawazumi and Morita, with an earlier appearance attributed to Morita; it remains open.