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## The distribution of sandpile groups of random graphs

- M. Wood
- Mathematics
- 20 February 2014

We determine the distribution of the sandpile group (a.k.a. Jacobian) of the Erd\H{o}s-R\'enyi random graph G(n,q) as n goes to infinity. Since any particular group appears with asymptotic… Expand

## On the probabilities of local behaviors in abelian field extensions

- M. Wood
- MathematicsCompositio Mathematica
- 23 November 2008

Abstract For a number field K and a finite abelian group G, we determine the probabilities of various local completions of a random G-extension of K when extensions are ordered by conductor. In… Expand

## Discriminants in the Grothendieck Ring

We consider the "limiting behavior" of *discriminants*, by which we mean informally the locus in some parameter space of some type of object where the objects have certain singularities. We focus on… Expand

## Parametrization of ideal classes in rings associated to binary forms

- M. Wood
- Mathematics
- 27 August 2010

We give a parametrization of the ideal classes of rings associated to integral binary forms by classes of tensors in $\mathbb Z^2\tensor \mathbb Z^n\tensor \mathbb Z^n$. This generalizes Bhargava's… Expand

## Random integral matrices and the Cohen-Lenstra heuristics

- M. Wood
- MathematicsAmerican Journal of Mathematics
- 16 April 2015

Abstract:We prove that given any $\epsilon>0$, random integral $n\times n$ matrices with independent entries that lie in any residue class modulo a prime with probability at most $1-\epsilon$ have… Expand

## THE DENSITY OF DISCRIMINANTS OF S3-SEXTIC NUMBER FIELDS

- M. Bhargava, M. Wood
- Mathematics
- 12 October 2007

. We prove an asymptotic formula for the number of sextic number fields with Galois group S 3 and absolute discriminant < X. In addition, we give an interpretation of the constant in the formula in… Expand

## Rings and ideals parameterized by binary n‐ic forms

- M. Wood
- MathematicsJ. Lond. Math. Soc.
- 30 July 2010

TLDR

## Moduli Spaces for Rings and Ideals

- M. Wood
- Mathematics
- 2009

The association of algebraic objects to forms has had many important applications in number theory. Gauss, over two centuries ago, studied quadratic rings and ideals associated to binary quadratic… Expand

## Belyi-Extending Maps and the Galois Action on Dessins d'Enfants

- M. Wood
- Mathematics
- 30 April 2003

We study the absolute Galois group by looking for invariants and orbits of its faithful action on Grothendieck’s dessins d’enfants. We define a class of functions called Belyi-extending maps, which… Expand

## Mass formulas for local Galois representations to wreath products and cross products

- M. Wood
- Mathematics
- 29 April 2008

Bhargava proved a formula for counting, with certain weights, degree n etale extensions of a local field, or equivalently, local Galois representations to S_n. This formula is motivation for his… Expand

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