I am an Assistant Professor at the University of Wisconsin-Madison and an American Institute of Mathematics Five-Year Fellow. I am also supported by National Science Foundation grants DMS-1147782 and DMS-1301690.
My research is in number theory and algebraic geometry. I am interested in explicit descriptions of moduli spaces for algebras and modules for those algebras. In number theory, these descriptions are useful for parametrizing orders in number fields and ideal classes of those orders. In algebraic geometry, the work can be viewed as understanding moduli of abstract points, or alternatively as parametrizing finite covers and line bundles on those covers. I am also interested in the applications to questions of counting number theoretical objects such as number fields and class groups. I am also more generally interested in moduli spaces and in the interplay between number theory and algebraic geometry. Currently, I am interested in algebraic geometry over finite fields, and in particular counting questions for varieties over finite fields, along with motivic analogs of these counting questions.
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.
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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.
I am currently supervising undergraduates and a graduate student (Summer 2013 and Fall 2013) on a research project funded by NSF grants DMS-1147782 and DMS-1301690.
I have supervised undergradutes in the past working on research projects with me through the Undergraduate Research Scholars Program.
I also supervised a group of undergraduates in Summer 2012 on research projects continuing the work from Math 490.
The UW Algebraic Geometry Seminar