tt*-geometry and Hermitian structures on the big phase space

The big phase space is an infinite dimensional manifold which is the arena
for topological quantum field theories and quantum cohomology (or
equivalently, dispersive integrable systems). tt*-geometry was introduced by
Cecotti and Vafa and is a way to introduce an Hermitian structure on what
would be naturally complex objects, and the theory has many links with
singularity theory, variation of Hodge structures, Higgs bundles, integrable
systems etc.. In this talk the two ideas will be combined to give a
tt*-geometry on the big phase space.

(joint work with Liana David)