Kevin Hutchinson

Student selection of random digits

The paper describes an investigation in which four groups of university students, of sizes 228, 111, 51 and 68, were asked to generate randomly a sequence of 25 digits from {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. Previous studies of this kind have suggested that people have tendencies to avoid repetition, to respond serially and to cycle. The aim of our investigation was to study further the nature and extent of peoples biases. Particular emphasis was put on the frequency and spread of digits in a selection, as well as on aspects of repetition and clustering. The distribution of the number of clusters of size k was obtained, and our analysis includes the use of this distribution. Our results support previous research showing the very special (and less favoured) status of 0 but also show a strong tendency of students to balance selections and to avoid clustering and sequentially repeating digits.

A Note on Milnor–Witt K-Theory and a Theorem of Suslin

We give a simple presentation of the additive Milnor–Witt K-theory groups of the field F, for n ≥ 2, in terms of the natural small set of generators. When n = 2, this specializes to a theorem of Suslin which essentially says that .

Hecke actions on the K-theory of commutative rings

Abstract We prove that in the case of a Galois extension of commutative rings R ⊂- S with Galois group G , the correspondence H → K i ( S H ) ( H ≤ G ) defines a cohomological G -functor. This gives a partial generalisation of results of Roggenkamp, Scott and Verschoren who consider the case of Picard groups. We use the equivalence of cohomological G -functors and Hecke actions (Yoshida, 1983) to derive some results about the structure of K -theory groups of rings of algebraic integers.

On the third homology of SL_2 and weak homotopy invariance

The goal of the paper is to achieve - in the special case of the linear group SL_2 - some understanding of the relation between group homology and its A^1-invariant replacement. We discuss some of the general properties of A^1-invariant group homology, such as stabilization sequences and Grothendieck-Witt module structures. Together with very precise knowledge about refined Bloch groups, these methods allow to deduce that in general there is a rather large difference between group homology and its A^1-invariant version. In other words, weak homotopy invariance fails for SL_2 over many families of non-algebraically closed fields.

Lines crossing a tetrahedron and the Bloch group

This survey paper is based on my IMPANGA lectures given in the Banach Center, Warsaw in January 2011. We study the moduli of holomorphic map germs from the complex line into complex compact manifolds with applications in global singularity theory and the theory of hyperbolic algebraic varieties.We give a light introduction to some recent developments in Mori theory, and to our recent direct proof of the finite generation of the canonical ring.We introduce a variety

A new approach to Matsumoto's theorem

\hat{G}_2

A Bloch-Wigner complex for SL 2

parameterizing isotropic five-spaces of a general degenerate four-form in a seven dimensional vector space. It is in a natural way a degeneration of the variety

The 2-Sylow Subgroup of the Wild Kernel of Exceptional Number Fields

G_2

The third homology of the special linear group of a field

, the adjoint variety of the simple Lie group

Homology stability for the special linear group of a field and Milnor-Witt K-theory

\mathbb{G}_2