Post-docs: Former and Current

Jesse Kass (2009 PhD Harvard University).
Jesse, who wrote his PhD with Joe Harris, is an RTG post-doc who works on extending families of Jacobians. I am looking forward to learning a lot from him.

Karl Schwede (2006 PhD University of Washington),
Karl was hired as an RTG-postdoc, but the next year won the NSF post-doctoral fellowship, which he now holds until 2010. So far, together with Sandor Kovacs, we've proved a simple new characterization of DuBois singularities in the Cohen-Macaulay case, which has nice applications to a conjecture of Kollar and to Kodaira vanishing for log canonical varieties. Karl and I also figured out a nice story about globally F-regular varieties and their relationship to Log Fano varieties. He has done deep work in several directions; my personal favorite is his work on F-adjunction and centers of F-purity, which brings to commutative algebra some powerful ideas from birational geometry. Check out his papers on the arvix

Howard Thompson (2002 PhD UC Berkeley)
With Howard, we worked out formulas for multiplier ideals of ideals defining nice subschemes of a smooth scheme, including any scheme defined by binomials (or more generally, any ideal admitting a "factorizing resolution" obtained by blowing up a monomial ideal). We also are studying  which exceptional divisors in the resolution of a  curve on a smooth surface are irrelevent from the point of view of computing jumping numbers, a question inspired by Wim Veys.

Russell Goward (2001 PhD University of Missouri)
Russell and I worked out the reduced scheme structure of the jet schemes of monomial schemes in a preprint called "Jet schemes of monomial ideals." (see preprint list).

Ana Bravo (1998 PhD Madrid), currently a professor of mathematics at the Autonoma in Madrid, Spain.
With Ana, we worked on two topics:
the behavior of the test ideal under smooth and etale maps (see preprint list),
and also on multiplier ideals for singular varieties (in progess). 

There are many other post-docs at the University of Michigan in the algebra and algebraic geometry groups with whom I have had "unofficial" working relationships.