Melanie Matchett Wood

The main focus of my research is in number theory and algebraic geometry, but it also involves work in probability, additive combinatorics, and algebraic topology. My PhD work found new explicit descriptions of moduli spaces for algebras and modules for those algebras. In number theory, these descriptions are useful for parametrizing orders in number fields and ideal classes of those orders. In algebraic geometry, the work can be viewed as understanding moduli of abstract points, or alternatively as parametrizing finite covers and line bundles on those covers. I am also interested in the applications to questions of counting number theoretical objects such as number fields and class groups. Motivated by this interest, I have been developing tools in probability theory to study randomly arising finite groups, such as the Jacobians of random graphs. In recent years, I have been very interested in the question of the distribution of the number of points on curves over a fixed finite field, both in special families, where we are able to prove results, and in general, where developing heuristics and conjectures is the cutting edge. This has also motivated my interest in building stronger general tools to determine limiting distributions of points on varieties over finite fields. I am also interested in algebro-geometric analogs of these counting questions, where the "counting" happens in the Grothendieck ring of varieties and there are strong connections to homological stability in algebraic topology.Publications:

Matchett Wood
Princeton University
2 009
Assistant Professor
Research Interests: 
Number Theory and Algebraic Geometry
Melanie Matchett Wood