Upper semicontinuity conjecture for invariants of singularities

Let $(Y,y)$ be a singularity, and let $w_{j}^i(y)$, $\bar{w}_{j}^i(y)$, and $\ell_{j}^i(y)$ denote the invariants defined from the mixed Hodge structures associated with the singularity. Upper semicontinuity conjecture. The invariants $w_{j}^i(y)$, $\bar{w}_{j}^i(y)$, and $\ell_{j}^i(y)$ are upper semicontinuous. These invariants measure limiting and intersection-cohomological data of singularities; the conjecture asks that they vary upper semicontinuously in families, extending the familiar semicontinuity properties of related cohomological invariants.