Teaching Fall 2023:


About Me

I am a Professor of Mathematics at the University of California San Diego, where I have been since 2005. Before that I was a C. L. E. Moore Instructor at MIT (2003-2005) and an NSF Postdoctoral fellow at the University of Washington (2002-2003). I was a graduate student at the University of Michigan (1997-2002), where I studied with Toby Stafford.

My research is in noncommutative algebra. In particular I study noncommutative graded rings, and the theory of noncommutative projective geometry.

Please use the tabs above to find more detailed information about my research and teaching.

Math 200 lecture notes

I wrote lecture notes with exercises to accompany Math 200AB, the first two quarters of our graduate abstract algebra sequence at UCSD. The topics are group theory, basic ring theory, module theory, and field theory. They are freely available below.

Math 200AB course notes

MSRI notes on noncommutative geometry

I wrote lecture notes, together with exercises, for a series of five lectures on noncommutative projective geometry which I gave at the MSRI graduate workshop in Berkeley in June 2012. These have now been published as a chapter of a joint book together with the other lecturers at the workshop:

Noncommutative Algebraic Geometry
by Gwyn Bellamy, Daniel Rogalski, Travis Schedler, J. Toby Stafford, & Michael Wemyss
Series: Mathematical Sciences Research Institute Publications
Publisher: Cambridge University Press
ISBN-13: 978-1107570030

An older version of my notes can be found on the arxiv, but note that the final published version has some minor corrections and additions.