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
Fall 2019: I am organizing the number theory learning seminar at Berkeley on the topic of arithmetic statistics of function fields via Hurwitz spaces.
The Berkeley Arithmetic Geometry and Number Theory Seminar (RTG Seminar)
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.