Some Applications of Non-Abelian Hodge Theory

Explore a comprehensive lecture on applications of non-abelian Hodge theory to meromorphic flat bundles and holonomic D-modules, inspired by Kontsevich's work. Delve into a generalization of the Barannikov-Kontsevich theorem on twisted de Rham cohomology. Review the concept of irregular Hodge filtration and its application to Kontsevich's conjecture about cohomologically rigid holonomic D-modules. Examine the boundedness of families of meromorphic flat bundles. Gain insights from Takuro Mochizuki of RIMS, Kyoto University, in this hour-long presentation at the Institut des Hautes Etudes Scientifiques (IHES).