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, seamless parameterization, locally-and-globally injective mappings, shape interpolation, and image retargeting. My research relies on several mathematical and computational tools such as: complex analysis, discrete differential geometry, computational conformal geometry, quasiconformal Teichmüller theory, harmonic mappings, 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). My research up to date focused mainly on better understanding and representing shape and developing novel methods to preserve shape under large deformations.