Time: 9h00-10h00, Thursday, September 23, 2021 (Vietnam time).

Link Online: meet.google.com/zsh-jnxc-eit

Abstract: The theory of mixed Hodge modules is a "Hodge theory on constructible sheaves", which contains the classical Hodge theory, the theory of variation of Hodge structures and Deligne's mixed Hodge theory. Since this theory is based on the theory of regular D-modules (D is the ring of differential operators), we can not apply it to irregular D-modules. The irregular Hodge theory allows us to equip some irregular D-modules with natural filtrations, called the irregular Hodge filtrations. For example, it defines ``the Hodge structure of a Landau-Ginzburg model'' and it is expected to have applications in the study of mirror symmetry. In general, the irregular Hodge filtration is very difficult to calculate and its properties are not fully understood. So, we begin by observing ``simple'' objects: the irregular Hodge filtration of the Fourier-Laplace transformation of monodromic mixed Hodge modules.

In this talk, I will briefly review the mixed Hodge module theory and irregular Hodge theory.

Then, I introduce the definition and properties of monodromic mixed Hodge modules, and give our result on the description of monodromic mixed Hodge modules. Finally, as an application of it, I will explain the computation of the irregular Hodge filtration of the Fourier-Laplace transformation of monodromic mixed Hodge modules.

This talk is based on https://arxiv.org/abs/2012.14671.