Jeffrey D. Achter

Using network properties to predict disease dynamics on human contact networks.

Recent studies have increasingly turned to graph theory to model more realistic contact structures that characterize disease spread. Because of the computational demands of these methods, many researchers have sought to use measures of network structure to modify analytically tractable differential equation models. Several of these studies have focused on the degree distribution of the contact network as the basis for their modifications. We show that although degree distribution is sufficient to predict disease behaviour on very sparse or very dense human contact networks, for intermediate density networks we must include information on clustering and path length to accurately predict disease behaviour. Using these three metrics, we were able to explain more than 98 per cent of the variation in endemic disease levels in our stochastic simulations.

The distribution of class groups of function fields

Abstract For any sufficiently general family of curves over a finite field F q and any elementary abelian l -group H with l relatively prime to q, we give an explicit formula for the proportion of curves C for which Jac ( C ) [ l ] ( F q ) ≅ H . In doing so, we prove a conjecture of Friedman and Washington.

The integral monodromy of hyperelliptic and trielliptic curves

We compute the

Split reductions of simple abelian varieties

\mathbb{Z}/\ell

ON DESCENDING COHOMOLOGY GEOMETRICALLY

and

A heuristic for the distribution of point counts for random curves over a finite field

\mathbb{Z}_{\ell}