Classification of monodromic mixed Hodge modules on C

Thời gian: 9h00-10h00, thứ Tư, 22/7.

Địa điểm: Phòng 301 nhà A5.

Abstract：In general, mixed Hodge modules are highly intricate objects, and there are only a few situations in which one can give a concrete description of what mixed Hodge modules actually look like.

In my previous work, it was shown that mixed Hodge modules on C with singularities only at the origin, called monodromic mixed Hodge modules, can be described by linear algebraic data given by their nearby and vanishing cycles with the morphisms between them.

The aim of this talk is to refine this description. It is known that monodromic perverse sheaves on $\mathbb{C}$ admit a classification into four basic types. In the setting of mixed Hodge modules, we explain that any monodromic mixed Hodge module can be described as a deformation of a direct sum of some basic mixed Hodge modules associated with these four types.