Melanie Matchett Wood

Professor of Mathematics at Harvard University
Radcliffe Alumnae Professor at the Radcliffe Institute for Advanced Study

I am currently on leave from the University of California, Berkeley.

My work is currently supported by a Packard Fellowship for Science and Engineering and National Science Foundation CAREER grant DMS-1652116.

Much of my research is motivated by questions in number theory, though the mathematics I study also includes arithmetic and algebraic geometry, topology, probability, and random groups. I am interested in understanding 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. I work on questions including 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 leads to questions in topology about certain moduli spaces of curves). To understand the distribution of class groups and Galois groups of unramified extensions, I also study random abelian and non-abelian groups to construct the random groups that are relevant for number theory and understand their properties. I have also been developing tools in probability theory to study randomly arising finite groups, such as the Jacobians of random graphs and cokernels of random matrices.

I completed my PhD at Princeton University in 2009 under the supervision of Manjul Bhargava, and was a Szego Assistant Professor at Stanford University from 2009-2011. I was an American Institute of Mathematics Five-Year Fellow from 2009-2017. I was faculty at the University of Wisconsin-Madison from 2011-2019. In Fall 2018, I was a Minerva Distinguished Visitor at Princeton University. Starting in Fall 2019, I have been faculty at the University of California, Berkeley. Starting in Fall 2020, I am faculty at Harvard University.

email: (you will have to replace "symbol" as appropriate)
mmwood symbol math symbol harvard symbol edu

My CV.

Publications and Preprints

PhD Students

Jiuya Wang, 2018 PhD, Foerster-Bernstein Postdoctoral Fellow and Phillip Griffiths Assistant Research Professor at Duke University
Megan Maguire, 2018 PhD, Postdoc at University of California-Irvine
Weitong Wang, in progress
Kristina Nelson, in progress
Anya Michaelsen, in progress

Notes for graduate students considering working with me.

Editorial Work

I am an editor of:
Journal of the American Mathematical Society. Follow the directions here to submit a paper.
Duke Mathematical Journal. Follow the directions here to submit a paper.
Algebra and Number Theory. Follow the directions here to submit a paper.
International Mathematics Research Notices. Follow the directions here to submit a paper.
Research in Number Theory. Follow the directions here to submit a paper.
I am no longer an editor of Journal de Théorie des Nombres de Bordeaux.


(Course materials available on Canvas.)

Fall 2020: MATH 273X: Distributions of Class Groups of Global Fields Problem Sets

Spring 2021: MATH 124: Number Theory


The Harvard Number Theory Seminar

The Berkeley Arithmetic Geometry and Number Theory Seminar (RTG Seminar)

Fall 2019: Informal random groups working group, meets Wednesdays from 1-2PM in 1032 (no meeting Oct 23, second meeting Oct 30)

Fall 2019: I am organizing the number theory learning seminar at Berkeley on the topic of arithmetic statistics of function fields via Hurwitz spaces.

Spring 2019: An informal learning seminar on the analogy between number fields and 3-manifolds


We had a conference about recent exciting connections between topology and number theory called Workshop on Arithmetic Topology at PIMS (Pacific Institute of the Mathematical Sciences) in Vancouver, June 10-14, 2019.

Now onto two dimensions, we are having a conference on the Geometry and Arithmetic of Surfaces in Madison February 9-10, 2019.

We had a conference on the Arithmetic of Algebraic Curves in Madison, April 6-8, 2018.

Notes for those who are asking me to write a letter of recommendation
A short reminder to myself about How to determine the splitting type of a prime (from the permutation representation of the decomposition and inertia groups).