Research Interests
- representation theory; symplectic geometry; equivariant forms and equivariant cohomology; quaternionic analysis
My current research involves quaternionic analysis ("calculus over quaternion numbers"), representation theory (a study of symmetries) and Feynman diagrams (a pictorial way of describing possible outcomes of interactions of subatomic particles in the context of quantum field physics). I am particularly interested in identifying the representation theoretic meaning of Feynman diagrams using the setting of quaternionic analysis. Along the way, I develop quaternionic analysis from the point of view of representation theory. Some of my results can be generalized to higher dimensions in the setting of Clifford analysis. I am also interested in geometric methods in representation theory.
My previous research involves equivariant forms and equivariant cohomology. In particular, I have found a generalization of the Berline-Vergne localization formula to non-compact (real reductive) Lie groups. Doing so involves characteristic cycles of sheaves and D-modules.
