Hodge theory and spectral sequences

Spectral and Hodge Theory of ‘witt’ Incomplete Cusp Edge Spaces

Incomplete cusp edges model the behavior of the Weil-Petersson metric on the compactified Riemann moduli space near the interior of a divisor. Assuming such a space is Witt, we construct a fundamental solution to the heat equation, and using a precise description of its asymptotic behavior at the singular set, we prove that the Hodge-Laplacian on differential forms is essentially self-adjoint, ...

Hodge Theory and Representation Theory

Normal form theory and spectral sequences

The goal of this paper is to show that spectral sequences give us a natural language in which to describe the process of computing the unique normal form. For a solid modern introduction to normal form theory and its historical development, see [Mur03b]. Although this is in no way intended as a review of (unique) normal form theory, let me give the reader some references to the literature which...

Hodge Theory and Geometry

This expository paper is an expanded version of a talk given at the joint meeting of the Edinburgh and London Mathematical Societies in Edinburgh to celebrate the centenary of the birth of Sir William Hodge. In the talk the emphasis was on the relationship between Hodge theory and geometry, especially the study of algebraic cycles that was of such interest to Hodge. Special attention will be pl...

Residues and Hodge theory

We discuss some basic applications of higher dimensional residues as presented in [7] and [8, Chap. V].