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. I was faculty at the University of Wisconsin-Madison from 2011-2019. In Fall 2018, I was a Minerva Distinguished Visitor at Princeton University.
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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
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.