In the past 15 years most of my
research has been an evolving study of symmetric spaces, their representations
and applications. Symmetric spaces are also known as symmetric varieties or
symmetric k-varieties when the base field k is not algebraically
closed. These symmetric spaces play an important role in many areas of mathematics,
including geometry, singularity theory and the cohomology of arithmetic subgroups.
They are probably best known, however, for their role in representation theory.
My work in symmetric varieties over algebraically closed fields includes geometric / invariant theoretical questions, as well as computational aspects. Much of my work on symmetric k-varieties was motivated by studying p-adic symmetric k-varieties and their representations. Other fields of interest to me, include integrable systems, computer algebra, combinatorics, graph theory and alternating forms.
Current Reseach Projects: