I am interested in theoretical and computational methods in geometry and their applications to problems in computer graphics and digital geometry processing.

My research focuses on better understanding and representing shape, and developing novel methods for preserving shape under large deformations.

In particular, I have published papers on the following applications: interactive shape and image deformation, bounded distortion mappings, surface and volume parameterization, generalized barycentric coordinates, shape interpolation and animation, and computation of geodesics on manifolds. Three of my papers received the best paper award from the Eurographics Association, as did my Ph.D. thesis. 17 of my papers have been published in ACM Transactions on Graphics, the foremost peer-reviewed journal in computer graphics.

My research draws heavily on various mathematical fields such as differential geometry, topology, complex and harmonic analysis, conformal geometry, and linear algebra. I adapt mathematical concepts from the smooth to the discrete case, where computational methods can be applied to solve real-world problems.

A major challenge is to design efficient and accurate numerical methods to solve the underlying optimization problems, which are often nonconvex. My recent research efforts have been to reduce such hard problems to convex or near-convex problems by applying a sophisticated change of variables or by decomposing the problem into smaller problems that are easier to solve.

In addition, I am enthusiastic about highly efficient general-purpose computations on parallel architectures, where many of my works use modern graphics processing units (GPU) to accelerate computations.