My current research is focused on shape representation, specifically on developing accurate and computationally efficient methods to do so. In recent years, new representations have been proposed to address the shortcomings of existing approaches. One such idea is the use of implicit representations with neural networks (IGR). Another idea is the use of elastic metrics on non-smooth curves, which may allow for the solution of inverse problems formulated directly in terms of them.
In general, I am interested in (discrete) differential geometry and geometric measure theory.