My research interests lie at the interface of conformal field theory, complex analytic Teichmueller theory, and geometric function theory. This work is partly motivated by the program of using vertex operator algebras to rigorously construct conformal field theory in the sense of G. Segal. Most recently I am involved in a project on algebraic structures and random geometry of stochastic lattice models.

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Key Terms: Teichmüller and moduli space theory or bordered Riemann surfaces. Mathematical foundation and construction of conformal field theory. Geometric function theory. Vertex operator algebras. Rigged Riemann surfaces, Weil-Petersson metric, quasiconformal mappings, sewing / gluing, conformal welding, lambda-lemma, Schiffer variation, determinant line bundles, and modular functors.