In 2018-2019 I will be a member at the Institute for Advanced Study; after that, I will be an Assistant Professor at the University of Georgia. I completed my PhD at Stanford in 2015; from 2015-2018 I was an NSF Postdoc at Columbia.
Broadly speaking, I am interested in the interplay between algebraic geometry and number theory (and, to a lesser extent, topology). Most of my work has focused on using arithmetic techniques to study classical questions about, for example, complex algebraic varieties. Currently, I am thinking about the arithmetic structures on the fundamental group of an algebraic variety, and the relationships between those structures and the geometry of the variety. Some of my other interests include questions about positivity and vanishing theorems, dynamics of algebraic varieties, and Hodge theory (broadly construed).
On this website you can find my publications and preprints, some talk notes and slides, some expository notes, and information on my teaching. I've included some non-mathematical writing. There's also an embryonic blog, which may or may not be updated. Finally, I'm trying a little experiment -- I'll try to keep a list of open questions that come up in my work, which is likely not up to date.