In the past 10 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 infinite dimensional flag varieties, Caylely graphs and alternating forms.

Research Overview

Current Reseach Projects:

• Structure of p-adic symmetric spaces
• Representations associated with p-adic symmetric spaces
• Invariant theory and geometry of symmetric varieties
• Computational work
• Hilbert Flag Varieties
• Cayley graphs

Publications