We propose a Hodge field theory construction that captures algebraic properties of the reduction of Zwiebach invari-ants to Gromov-Witten invariants. It generalizes the Barannikov-Kontsevich construction to the case of higher genera correlators with gravitational descendants. We prove the main theorem stating that algebraically defined Hodge field theory correlators satisfy all tautological rel...

I will report on joint work with Eric Leichtnam, Rafe Mazzeo, and Paolo Piazza extending and refining Cheeger’s study of ideal boundary conditions for the de Rham operator from the case of isolated conic singularities to arbitrary stratified pseudomanifolds. This leads to a notion of ‘mezzoperversity’ intermediate between the upper and lower perversities of Goresky-MacPherson. If time permits, ...

In the framework of an extended BRST formalism, it is shown that the four (3 + 1)-dimensional (4D) free Abelian 2-form (notoph) gauge theory presents an example of a tractable field theoretical model for the Hodge theory.

We discuss the Becchi-Rouet-Stora-Tyutin (BRST) cohomology and Hodge decomposition theorem for the two dimensional free U(1) gauge theory. In addition to the usual BRST charge, we derive a local, conserved and nilpotent co(dual)-BRST charge under which the gauge-fixing term remains invariant. We express the Hodge decomposition theorem in terms of these charges and the Laplacian operator. We tak...

This paper wishes to foster communication between mathematicians and physicists working in mirror symmetry and orbifold Gromov-Witten theory. We provide a reader friendly review of the physics computation in [ABK06] that predicts Gromov-Witten invariants of [C/Z3] in arbitrary genus, and of the mathematical framework for expressing these invariants as Hodge integrals. Using geometric properties...

A differential geometrical and topological structure of Delsarte transmutation operators in multidimension is studied, the relationships with De Rham-Hodge-Skrypnik theory of generalized differential complexes is stated.