Melanie Matchett Wood

Biosketch

Melanie Matchett Wood is the William Caspar Graustein Professor of Mathematics at Harvard University. She received her BS in Mathematics from Duke University, and her PhD in Mathematics from Princeton University. Following an American Institute of Mathematics Five-Year Fellowship and a Szëgo Assistant Professorship at Stanford University, she held faculty appointments at the University of Wisconsin–Madison and the University of California, Berkeley before joining Harvard in 2020. Wood has received a Sloan Research Fellowship, a Packard Fellowship for Science and Engineering, a Presidential Early Career Award for Scientists and Engineers, the National Science Foundation’s Alan T. Waterman Award, and a MacArthur Fellowship. She is a Fellow of the American Mathematical Society, an Honorary Member of the London Mathematical Society, and a member of the American Academy of Arts & Sciences.

Research Interests

Melanie Matchet Wood’s research program is motivated by questions in number theory and arithmetic statistics specifically. Her work spans number theory, arithmetic and algebraic geometry, topology, probability, and random groups. She works to understand the distribution of number fields and their fundamental structures, including class groups, p-class tower groups, and the Galois groups of their maximal unramified extensions. She investigates questions of counting number fields, finding the average number of unramified G-extensions that number fields have, bounding the sizes of class groups, and function field analogs of all of these questions (which then lead to questions in topology about certain moduli spaces of curves). To understand the distribution of class groups and Galois groups of unramified extensions, she also studies random abelian and non-abelian groups to construct the random groups that are relevant for number theory and understand their properties. She has developed tools in probability theory to study randomly arising groups (and other algebraic objects) in much more general settings, such as the fundamental groups of 3-manifolds, Jacobians of random graphs, and cokernels of random matrices.