Department of Mathematics

University of Wisconsin-Madison

In Fall 2018, I was a Minerva Distinguished Visitor at Princeton University.

My work is currently supported by a Packard Fellowship for Science and Engineering, a Sloan Research Fellowship, 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.

**email:** (you will have to replace "symbol" as appropriate)

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My CV.

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

Algebra and Number Theory. Follow the directions here to submit a paper.

Journal de Théorie des Nombres de Bordeaux. Follow the directions here to submit a paper.

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.

In Fall 2016, I taught Math 748, Algebraic Number Theory.

In Fall 2014, I taught Math 748, Algebraic Number Theory.

In Spring 2014, I taught Math 222 (two classes), Calculus and Analytic Geometry.

In Spring 2012, I taught Math 490: Collaborative Undergraduate Research Lab.

In Fall 2011, I taught Math 847: Algebraic Curves and Varieties over Finite Fields.

The UW Number Theory and Representation Theory Seminar

The UW Algebraic Geometry Seminar

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).