Kähler hyperbolicity and $L_2$-Hodge theory

Hodge Theory and Representation Theory

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].

Gauge Theory as Hodge Theory

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.

Hodge-Tate Theory

This thesis aims to expose the amazing sequence of ideas, concerning p-adic representations coming from geometry, that form the heart of what was called Hodge-Tate theory. This subject, initiated by Tate in the late ’60s in analogy to classical Hodge theory, leads in to the now vast and highly fruitful program of p-adic Hodge Theory. The central result of the theory is the Hodge-Tate decomposit...