Welcome!

I'm a J.L. Doob Professor of Mathematics at the University of Illinois at Urbana-Champaign. I finished my Ph.D. under the direction of Ravi Vakil at Stanford in 2007.

My basic research interests are number theory and algebraic geometry, though more specifically I'm interested in Galois module structures of 'interesting' objects and Hilbert 90-like results. You can find copies of papers and preprints for my work on my research page.

I also enjoy teaching a great deal, and have had the good fortune of teaching both calculus and linear algebra while at Stanford. Links for the classes I have taught so far can be found on my teaching page.

To the right you see a picture of me which has been compressed using the singular value decomposition from linear algebra. If you put your mouse over the image you can see the image compressed using singular values up to 41. Don't know about this amazing theorem or why it should allow you to compress images? I have a quick overview of the theory available here.