We shall discuss ongoing investigations about some applications of non-abelian Hodge theory to the study of meromorphic flat bundles and more general holonomic D-modules, inspired by Kontsevich. The plan is as follows. First, we discuss a generalization of Barannikov-Kontsevich theorem about twisted de Rham cohomology. Then, after reviewing irregular Hodge filtration which was motivated by the study of Kontsevich complexes, we explain its application to an evidence for a conjecture of Kontsevich about cohomologically rigid holonomic D-modules. We would also like to discuss a boundedness of families of some families of meromorphic flat bundles.
De Jorgen Ellegaard Andersen
De Alexander Goncharov
De Mina Aganagic
De Yan Soibelman
De Tony Pantev
De Kenji Fukaya
De Denis Auroux
De Davide Gaiotto
De Yuri Tschinkel
De Pavel Etingof
De Alexander Odesskii
De Barbara Schapira
De Barbara Schapira
