Séminaire de Mathématique

Quantum D-modules and mixed twistor D-modules

by Prof. Takuro MOCHIZUKI (RIMS, Kyoto University)

Amphithéâtre Léon Motchane (IHES)

Amphithéâtre Léon Motchane


Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette
Mixed twistor D-modules are D-modules with mixed twistor structure. The notion of twistor structure is a generalization of that of Hodge structure, introduced by C. Simpson. As in the Hodge case, various operations for D-modules are enhanced to those for mixed twistor D-modules. It implies that some important mathematical objects are naturally equipped with mixed twistor structure. For example, the D-modules associated to families of Laurent polynomials, called the GKZ hypergeometric systems, are naturally equipped with mixed twistor structure. It looks natural to pursuit their roles in the Hodge theoretic aspect of mirror symmetry. In this talk, I am planning to discuss the degeneration of twistor structure associated to the degeneration of Landau-Ginzburg models, and to explain how the isomorphism of Givental induces an isomorphism of mixed TEP-structures in the local mirror symmetry for Fano toric manifolds.