6 problems

Converse characterization conjecture. If $(\mathfrak{I}_{\hat\Psi},\mathfrak{t}_{\hat\Psi})$ is a commutative Frobenius algebra in

Mod-8 signature conjecture. The evaluation

Let $X^n$ be a space and let $p$ be a prime. Say that $H^*(X;\mathbb{Z}_p)$ is $k$-periodic up to degree $c$ when multiplication by a periodicity element induces successive isomorp…

Let ${\mathcal{M}}_\B^{{\bm \mu},{\bf r}}$ be the generic wild character variety, let $d_{{\bm \mu},{\bf r}}$ be its dimension, and let…

Let $M^m$ be a closed, smooth, oriented Riemannian manifold and let $N^n$ be a closed submanifold of codimension $m-n \geq 2$. Define the compact Riemannian manifold … where…

Hain and Looijenga's conjecture. These intersection pairings are perfect (Poincaré duality), and $R^{\bullet}_c(M_g)$ is a free $R^{\bullet}(M_g)$-module of rank one.