In this talk I will describe several approaches for learning on curved surfaces, represented as
point clouds or triangle meshes, undergoing non-rigid deformations. I will first give a brief
overview of geodesic convolutional neural networks (GCNNs) and their variants and then present a
recent approach based on diffusion. The key properties of this approach is that it avoids
potentially error-prone and costly operations with robust and efficient building blocks that are
based on learned diffusion and gradient computation. I will then show several applications, ranging
from RNA surface segmentation to non-rigid shape correspondence, while highlighting the invariance
of this technique to sampling and triangle mesh structure.