I am a Presidential Professor of Mathematics at the University of Pennsylvania.
My research generally concerns algebra and arithmetic geometry, in particular, the interactions between field arithmetic, algebraic objects such as division algebras and quadratic forms, and arithmetic and algebraic geometry.
In 2016, I was awarded a Presidential Early Career Award (PECASE) for my research by President Barack Obama. I was elected as a Fellow of the American Mathemtical Society in 2017.
Previously I was a professor of mathematics at Rutgers University and before that, at the University of Georgia. I was awarded the UGA Creative Research Medal in 2012, and the UGA Outstanding Professor Award in 2016.
Finite dimensional division algebras and the Brauer group, linear algebraic groups, algebraic cycles, and field theory.
I am particularly interested in the application of techniques and ideas from algebraic topology and algebraic geometry to problems in algebra.