Hodge theory and the Hilbert scheme

HILBERT MODULAR FORMS AND p-ADIC HODGE THEORY

We consider the p-adic Galois representation associated to a Hilbert modular form. Carayol has shown that, under a certain assumption, its restriction to the local Galois group at a place not dividing p is compatible with the local Langlands correspondence [C2]. In this paper, we show that the same is true for the places dividing p, in the sense of p-adic Hodge theory [Fo], as is shown for an e...

Matrix Theory, Hilbert Scheme and Integrable System

We give a reinterpretation of the matrix theory discussed by Moore, Nekrasov and Shatashivili (MNS) in terms of the second quantized operators which describes the homology class of the Hilbert scheme of points on surfaces. It naturally relate the contribution from each pole to the inner product of orthogonal basis of free boson Fock space. These basis can be related to the eigenfunctions of Cal...

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...

The Intrinsic Hodge Theory