Research and Teaching Statement

My research areas are design and analysis of algorithms, computational geometry, mesh gen-eration, and their applications. Geometric algorithms play a fundamental role in many areas such as scientic computing, graphics, visualization, computer aided design, computer vision, structural biology, and geographic information systems. The overall goal of my research is to understand the mathematical structure of problems in these areas; and to design, analyze and implement ecient algorithmic solutions with both theoretical bounds and good performance in practice. This enables me to have an inter-disciplinary impact on various scientic applications. Mesh Generation. A principal component of my research is meshes (triangulations), which are subdivisions of geometric domains into small and simple elements. Meshes are essential to numer-ical simulations. Two of their key requirements are to ensure that the shape of the mesh elements are of good quality and that the size of the mesh is small. Mesh element quality is critical in determining interpolation error in applications and hence is an important factor in the accuracy of the simulations as well as the convergence speed. Mesh size is also critical because between two meshes with the same quality bound, the one with fewer elements is generally preferred as it implies faster processing by the numerical algorithm in use. In collaboration with many researchers fro