My research primarily focused on the Ricci flow and its solitons prior to 2019. Since then, I have shifted my attention to geometric and analytic problems in manifold learning. 

• Recently, I have been studying the convergence of the Hessian estimator on data manifolds with Hau-Tieng Wu, and we could justify the convergence even for the boundary regions. We also analyze the continuous counterpart of the HLLE algorithm and offer insights for further investigation..

• On the other hand, together with my colleagues, we have made some discoveries regarding spherical MDS, suggesting that MDS may be related to certain classical minimal embeddings of RP^2.