5 problems

Let $R={\mathbb Z}[t]$ or $R={\mathbb Z}[t,t^{-1}]$, let $K(R)$ be the kernel of the evaluation map $SL_2(R)\to SL_2({\mathbb Z})$, and let ${\mathcal W}$ be the kernel of the indu…

Let $M$ be a simply connected compact Kähler manifold, let ${\mathscr M}$ be the moduli space of algebraic structures on the manifold underlying $M$, and let ${\mathcal G}_M$ be th…

Let ${\mathfrak u}_{g,n+\vec r}$ be the prounipotent Lie algebra of the relative completion, equipped with its weight filtration, and write $\operatorname{Gr}^W_m$ for its weight-…

For a partition ${\boldsymbol\mu}$ with at most $g$ parts, let $V_{\boldsymbol\mu}$ be the corresponding irreducible ${\mathrm{Sp}}(H)$-module, and let … be the homomorphism induce…

Let $H$ be the standard symplectic representation in genus $2$, let $V_\boxplus$ be the weight $-2$ ${\mathrm{Sp}}(H)$-module in the minimal presentation … and, after decomposing a…