A common mathematical structure recently appeared in various mathematical theories: the theory of quantization, that of quantum curves, that of quantum D-modules, that of tt*-structures, that of twistor D-modules, etc. Roughly speaking, this structure is a deformation family from a coherent sheaf on the cotangent bundle to a D-module.
"Generalized Hodge theory" is expected to be hidden as a reason for the appearance of such a structure, which should be an interesting part of "Quantum geometry".
There are several attempts toward generalized Hodge theory. For example, the theory of twistor D-modules gives us the functoriality of generalized Hodge structures on D-modules with respect to the six operations. However, it captures only one aspect of classical Hodge theory. Generalized Hodge theory will be much richer once it will be uncovered.
In this conference, we plan having survey and research talks by leading mathematicians who work in various related fields. They hopefully will help us to obtain deeper understanding of generalized Hodge theory.