Algebraic aspects in modular theory

Algebraic Aspects of Spectral Theory

We describe some aspects of spectral theory that involve algebraic considerations but need no analysis. Some of the important applications of the results are to the algebra of n× n matrices with entries that are polynomials or more general analytic functions. Short title: Algebraic Spectral Theory MSC subject classification: 47A56, 47C05, 15A22, 16Sxx, 16Bxx

Modular Forms and Algebraic K-theory

In this paper, which follows closely the talk given at the conference, I will sketch an example of a non-trivial element of K2 of a certain threefold, whose existence is related to the vanishing of an incomplete L-function of a modular form at s = 1. To explain how this fits into a general picture, we begin with a simple account, for the non-specialist, of some of the conjectures (mostly due to...

Constructive aspects of algebraic euclidean field theory

This paper is concerned with constructive and structural aspects of euclidean field theory. We present a C*-algebraic approach to lattice field theory. Concepts like block spin transformations, action, effective action, and continuum limits are generalized and reformulated within the C*-algebraic setup. Our approach allows to relate to each family of lattice models a set of continuum limits whi...

Algebraic aspects of higher nonabelian Hodge theory

Modular data: the algebraic combinatorics of conformal field theory

This paper is primarily intended as an introduction for mathematicians to some of the rich algebraic combinatorics arising in for instance conformal field theory (CFT). It is essentially self-contained, apart from some of the background motivation (Section I) and examples (Section III) which are included to give the reader a sense of the context. Detailed proofs will appear elsewhere. The theor...