Part 1 My main research interests are theoretical and computational methods in geometry and their applications to problems in computer graphics and digital geometry processing. In particular, I am working on the following applications: interactive shape and image deformation, parameterization and computer animation. My research relies on several mathematical and computational tools such as: complex analysis, discrete differential geometry, computational conformal geometry, quasiconformal Teichm?ller theory, partial differential equations, generalized barycentric coordinates and boundary element methods. In addition, I am enthusiastic about high efficiency general-purpose computations on parallel architectures such as modern graphics processing units (GPGPU). Part 2 My research up to date focused mainly on better understanding and representing shape and developing novel methods to preserve shape under large deformations.