Nigel Kalton's work in isometrical Banach space theory

This paper surveys some of the late Nigel Kalton's contributions to Banach space theory. The paper is written for the Nigel Kalton Memorial Website http://mathematics.missouri.edu/kalton/, which is scheduled to go online in summer 2011

New results on path-decompositions and their down-links

In a recent paper the concept of \emph{down-link} from a $(K_v,\Gamma)$-design \cB to a $(K_n,\Gamma')$-design \cB' has been introduced. In the present paper the spectrum problems for $\Gamma'=P_4$ are studied. General results on the existence of path-decompositions and embeddings between path-decompositions playing a fundamental role for the construction of down-links are also presented

On the Brownian gas: a field theory with a Poissonian ground state

As a first step towards a successful field theory of Brownian particles in interaction, we study exactly the non-interacting case, its combinatorics and its non-linear time-reversal symmetry. Even though the particles do not interact, the field theory contains an interaction term: the vertex is the hallmark of the original particle nature of the gas and it enforces the constraint of a strictly positive density field, as opposed to a Gaussian free field. We compute exactly all the n-point density correlation functions, determine non-perturbatively the Poissonian nature of the ground state and emphasize the futility of any coarse-graining assumption for the derivation of the field theory. We finally verify explicitly, on the n-point functions, the fluctuation-dissipation theorem implied by the time-reversal symmetry of the action.Comment: 31 page

Mixed Degree Number Field Computations

We present a method for computing complete lists of number fields in cases where the Galois group, as an abstract group, appears as a Galois group in smaller degree. We apply this method to find the 25 octic fields with Galois group PSL₂(7) and smallest absolute discriminant. We carry out a number of related computations, including determining the octic field with Galois group 2³:GL₃(2) of smallest absolute discriminant