Research


I study the topology of algebraic varieties, especially their singularities.  Most of my work involves intersection cohomology and more general perverse sheaves.  For many interesting spaces, such as flag varieties and toric varieties and their generalizations, intersection cohomology and perverse sheaves give important information about questions in representation theory and combinatorics. Much of my work involves finding explicit combinatorial methods to compute intersection cohomology and perverse sheaves on these spaces, in terms of combinatorial data provided by the symmetries and orbits of a group action.

MG: computing with moment graphs

Some time ago I wrote some Macaulay 2 code to compute (torus equivariant) intersection cohomology (and ordinary cohomology) for certain nice spaces including Schubert varieties, in terms of the "moment graph" or "1-skeleton" formed by the zero and one-dimensional orbits. The code is available here. It's far from a finished system, and sometimes I have had to make modifications or extensions for a particular computation. If there's something you would like to do with it that it doesn't currently do, let me know.

Some slides

Seminars and conferences

I am a co-organizer of the Representation Theory seminar at UMass, and I regularly attend the Valley Geometry Seminar.

Working seminar at UMass on quiver varieties and representation theory, Spring 2006

Tara Holm and I organized a special session "Combinatorial techniques in equivariant topology" at the Fall 2006 AMS meeting in Storrs, CT. Follow the link for abstracts and slides for many of the talks.