I study the topology of algebraic varieties, especially their singularities.  Most of my work involves intersection cohomology (IH) and more general perverse sheaves.  For many interesting spaces, such as flag varieties and toric varieties and their generalizations, IH and perverse sheaves give important information about questions in representation theory and combinatorics.

I am especially interested in making perverse sheaves, whose definition involves considerable homological algebra, more accessible and computable for these spaces.  The key fact is that these spaces have large groups of symmetries.  Equivariant intersection cohomology uses the action, giving a theory which is in many cases easily computable and which gives the ordinary IH as a by-product.  The computation of intersection cohomology then becomes an algorithm involving the combinatorics of the orbits under the group and simple commutative algebra.  The result of the computation is canonically and functorially isomorphic to intersection cohomology, which is important for applications which involve relations between intersection cohomologies of different spaces, such as computing extensions and more general perverse sheaves.

My CV (pdf format)            My publications                    Working seminar on quiver varieties and representation theory, Spring 2006

MG:  Macaulay 2 code to compute equivariant (intersection) cohomology with moment graphs

Slides from my talk at the Toric Topology conference, Osaka