**Post-docs: Former and Current**

Caleb Ashley (Howard, 2013) Caleb came to UM in 2017. Caleb's Phd thesis investigates discrete subgroups of the isometry group of the hyperbolic plane. We are hoping to collaborate on some projects about character varieties.

Eleonore Faber (2012 PhD Vienna). Eleonore arrived in 2015, but was offered a tenure track position at Leeds, where she will move summer 2017, shortly after arriving here. Eleonore's PhD thesis and training were on resolution if singularities, but her work since then has ben mainly in non-commutative algebra. With Greg Muller, we have proved that toric rings have a non-commutative resolution of singularities.

Greg Muller (2010 PhD Cornell). Greg was a UM post-doc 2013-2017, and is now moving onto to a tenure track position at the University of Oklahoma. Greg has broad interests, having gotten his start studying D-modules but more recently moved into algebro-geometric aspects of cluster algebras and Frobenius splitting. He is the inventor of the class of locally acyclic cluster algebras, which are much less pathological than arbitrary cluster algebras, but seem to include most of the main examples. With Greg's lead, together with Angelica Benito and Jenna Rajchgot, we proved that locally acyclic cluster algebras are strongly F-regular (type), which implies a host of other nice conditions including rational singularities. More recently, we are studying global dimension of rings of endomorphisms and differential operators for toric varities (with Eleonore Faber).

Jenna Rajchgot (2012 PhD Cornell). She was a post-doc at UM 2012-2015, and is now a tenure track assistant professor in her home country of Canada at the University of Sasketchewan. Jenna's research combinatorial commutative algebra and algebraic geometry, including things like quiver representations, Schubert varieties, Groebner basis, but also Frobenius splitting and characteristic p. She is amazing at getting Macaulay to do stuff! With Greg Muller and Angelica Benito, we studied on cluster algebras in characteristic p.

Angelica Benito (2010 PhD Madrid). Angelica was at UM 2011-2015, and is now at Autonoma in Madrid. We have been working on various issues of trying to use F-threshold and related invariants to measuring singularities for resolution of singularities in prime characteristic. We also worked on cluster algebras in characteristic p with Greg Muller and Jenna Raichgot.

Maria del Rocio Blanco Somolinos (2011 PhD La Universidad de Castilla-La Mancha). Rocio spent the fall 2011 working with me and Howard Thompson on issues of resolution of binomial ideals.

Bharghav Bhatt (2010 PhD Princeton). Hildebrandt Post-doc 2010-2012. Now back at UM as a professor!

Matt Satriano (2010 PhD Berkeley). Matt was an RTG/NSF post-doc 2010-20013. Now he an Assistant Professor at Waterloo. Matt works mostly on algebraic stacks and quotient singularities but has broad interests which extend from modului spaces to more combinatorially amd applied directions.

Jesse Kass (2009 PhD Harvard University). Jesse was an RTG post-doc 2009-20012, and is

now an assistant professor at University of South Carolina.

His current work focuses on abelian varieties, compactified Jacobians, moduli of sheaves and related topics.

Karl Schwede (2006 PhD University of Washington),

now professor at the University of Utah. He was a Michigan RTG/NSF post-doc 2006-2010.
At Michian, we worked on two different projects. 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. Karl is also collaborating with my PhD student Kevin Tucker, trying to understand how the test ideal behaves under finite maps.
Karl 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) is a professor at University of Michigan, Flint. He was a Michigan post-doc 2002-2006 (his final year on our RTG grant). 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.

See also his bio on Mathematicians of the African Diaspora.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). See also his bio on Mathematicians of the African Diaspora.

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.