5 problems

Positivity conjecture. The Novikov–Shubin invariants of $\bar X\to X$ are always positive; equivalently, the capacities are always finite.

Positivity conjecture for Novikov–Shubin invariants. The Novikov–Shubin invariants of a closed manifold are positive.

Torsion equality conjecture. The $L_2$-analytic and $L_2$-Reidemeister torsions of $M$ are equal.

Let $\Gamma$ be a group, and let $C_*$ be a chain complex of finitely generated free $\mathbb{Z}\Gamma$-modules. The Novikov–Shubin invariants of $C_*$ are the invariants associate…

The setting is a Riemannian foliation with a generalized Dirac operator $D$ along its leaves. Assume that the projection onto the kernel of $D$ and the spectral projections of…