Complex Analysis in Higher Dimensions

I am fascinated by various aspects of complex analysis in higher dimensions (called several complex variables – SCV). A plethora of new phenomena arise in SCV that are absent in the one variable setting. This can be attributed to the deep interplay between various branches of mathematics – analysis, geometry (algebraic, analytic, differential, metric, etc.), and PDEs to name just a few. My research focuses on exploring these connections in SCV in two specific contexts:

• domains in ℂn – boundary geometry, function theory, and invariant metrics, and

• CR singular manifolds – geometry and function theory.