Dissertation Defense: Using Mixed Hodge modules to Study Singularities

Abstract: Mixed Hodge modules have found many applications in algebraic geometry. They have been essential in the study of hypersurface singularities, for example, in the definition of Hodge ideals and minimal exponent. I will explain work that generalizes the results for hypersurfaces to higher codimension subvarieties. The main tool is the V-filtration of a mixed Hodge module along the subvariety Z. Our methods show that this filtration is suitably compatible with the Hodge and weight filtration of a mixed Hodge module, and that one can use the V-filtration to compute restriction functors for mixed Hodge modules. These restriction functors are applied to the study of local cohomology and to the Fourier-Laplace transform of monodromic mixed Hodge modules.

HYBRID Defense:
School of Ed Building, Room 2225
https://umich.zoom.us/j/96660837935?pwd=R1N0aC9OSDUxZjVYQ29LWTBDa2QyUT09