
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 kvarieties 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 kvarieties was motivated by studying padic
symmetric kvarieties and their representations. Other fields of interest
to me, include integrable systems, computer algebra, combinatorics, graph theory and alternating
forms.
Current Reseach Projects: