Iritani's Lecture:

Hodge theory of Landau-Ginzburg model and its quantization

A plan of my talk:

In my talk, I will focus on Hodge theoretic

mirror symmetry for toric varieties whose mirror

is known to be Landau-Ginzburg models.

We have A-model D-module (quantum cohomology)

from a toric variety and B-model D-module from its

Landau-Ginzburg mirror and the two D-modules are isomorphic.

Referring to several examples, I am planning to

explain the following (some of the topics may be omitted):

1. B-model D-module associated to the Landau-Ginzburg model

2. Comparison with the A-model D-module (Gromov-Witten


3. Different A-model geometries corresponding to the same

(global) B-model D-modules (e.g. crepant resolution conjecture).

4. Semi-infinite Hodge theory point of view

5. Givental's quantization in terms of Hodge theory