Rongjie Lai Rensselaer Polytechnic Institute In this talk, I will discuss our recent work of non-isometric matching for largely deformed shapes. Our method is based on Laplace-Beltrami basis pursuit via conformal deformation. My talk will further extend to introduce a new way of defining convolution on manifolds via parallel transport. This geometric way of defining convolution provides a natural combination of modeling and learning on manifolds. I will demonstrate its applications to shape matching using deep neural network based on parallel transportation convolution (PTC-net).