Post-docs: Former and Current
Dan Smolkin (Utah, 2019) Dan joins us after a year at Oklahoma. He works on F-singularities, symbolic powers of ideals, toric varieties and related topics.
Janet Page (UIC, 2018) Janet is an expert on characterstic p commutative algebra and toric geometry, especially Hibi Rings. We have been studying lower bounds on F-pure thresholds and extremal singularities.
Tim Ryan (UIC, 2016) Tim joins us after a RTG post-doc at Stony Brook. He works in birational geometry, the theory of moduli spaces, derived categories in algebraic geometry, and higher codimension cycles.
Caleb Ashley (Howard, 2013) Caleb came to UM in 2016 and now works at Boston College. 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 is now at the University of Leeds. 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 a tenure track professor the University of Oklahoma. Greg got 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, 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.
Jenna Rajchgot (2012 PhD Cornell). She was a post-doc at UM 2012-2015, and is now an Assistant professor 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 ICMAT in Madrid. She is an expert on resolution of singularities in prime characteristic. We worked 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). 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 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.
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 studied 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).