My work is supported by a Packard Fellowship for Science and Engineering, a National Science Foundation Waterman Award, and
a MacArthur Fellowship.
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 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.
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. In 2019-2020, I was faculty at the University of California, Berkeley. Since 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.
Jiuya Wang, 2018 PhD,
Assistant Professor at the University of Georgia
Megan Maguire, 2018 PhD, at Epic Systems
Weitong Wang, 2022 PhD, Lecturer, College of Mathematical Sciences of Harbin Engineering University
Anya Michaelsen, 2022 Masters, at Meta
Kristina Nelson, 2023 PhD
Michael Kural, 2025 PhD
Matt King, in progress
Elia Gorokhovsky, in progress
August Liu, in progress
Jack Miller, in progress
Sunny Zhang, in progress
Notes for graduate students considering working with me.
Fall 2025: MATH 223A: Algebraic Number Theory
2024-25 I am not teaching, as I am a Fellow at the Radcliffe Institute.
Fall 2023: MATH 223A: Algebraic Number Theory (Local Fields and Local Class Field Theory)
2022-23 I am not teaching, as I am a Fellow at the Radcliffe Institute.
Spring 2022: MATH 223B: Class Field Theory
Fall 2021: MATH 124: Number Theory
Spring 2021: MATH 124: Number Theory
Fall 2020: MATH 273X: Distributions of Class Groups of Global Fields Problem Sets
Arithmetic statistics seminar, Mondays 3-4PM in SC 507, this is the seminar for my group, everyone is welcome, and it is a good way to learn about what people at Harvard are thinking about in arithmetic statistics (email me to get on mailing list)
Harvard-MIT Algebraic Geometry 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: 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 organized a workshop Nilpotent counting problems in arithmetic statistics at AIM November 11-15, 2024.
I gave a course on Arithmetic Statistics at the Park City Math Institute in July 2022. Here are the notes for my PCMI course. (Comments and corrections welcome!) Here are the slides.
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.