My research fields are Differential Geometry, Symplectic Geometry and Global Analysis. Recently I have been working in Noncommutative Geometry, in particular on deformation quantization problems. Deformation quantization is a deformation theory of Poisson algebras, and has made significant advances in recent years. We solved the existence problem for deformation quantization of Poisson algebras of symplectic manifolds, after which Kontsevich provided a solution for general Poisson manifolds. We are currently focusing on convergence problems for deformation quantization, and have found mysterious phenomena not arising in formal deformation quantization. I am also interested in the geometry of infinite dimensional manifolds, and have an ongoing project investigating the geometry of loop spaces with my colleague, Professor Steven Rosenberg at Boston University.