Zoom link:  https://princeton.zoom.us/j/91248028438

Passcode: Number of plane conics tangent to five general plane conics.    

This describes joint work in progress with M. Mustata, in which we study the filtration on local cohomology sheaves induced by their natural mixed Hodge module structure. Special properties of this filtration, for instance strictness, lead to a number of different applications, including an injectivity theorem for dualizing complexes, local vanishing for forms with log poles, and especially a characterization of the local cohomological dimension of a closed subscheme in terms of  data arising from a log resolution of singularities.