# Rongjie Lai

#### Assistant Professor, Mathematical Sciences

Dr. Rongjie Lai received his B.S. degree in mathematics from the University of Science and Technology of China, in 2003, his M.S. degree in mathematics from the Academy of Mathematics and System Sciences, Chinese Academy of Sciences in 2006 and his Ph.D. degree in applied mathematics from the University of California, Los Angeles, in 2010. Before he joined RPI in 2014, Dr. Lai held visiting assistant professor positions at the University of Southern California and the University of California, Irvine, respectively.

Dr. Lai’s research interests are mainly in developing mathematical and computational tools for analyzing and processing signals, images as well as unorganized data using methods of variational partial differential equations, computational differential geometry and learning. His research further extends to the design of efficient numerical methods to solve variational PDEs and optimization problems. Dr. Lai’s research has wide applications in medical imaging, brain mapping, computer graphics, as well as their extensions to data science. In 2018, Dr. Lai was granted an NSF CAREER award for his research in geometry and learning for manifold-structured data in 3D and higher dimension.

B.S. in Mathematics, University of Science and Technology of China, 2003

M.S. in Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, 2006

Ph.D in Applied Mathematics, University of California, Los Angeles, 2010

- Geometric and learning for manifold-structured data
- Image processing and applications
- Optimization

- R. Lai, J. Li, “Manifold Based Low-rank Regularization for Image Restoration and Semi-supervised Learning”, Journal of Scientific Computing, 74(3), pp 1241–1263, 2018.
- R. Lai, J. Lu, “Point Cloud Discretization of Fokker-Planck Operators for Committor Functions”, Multiscale Modeling & Simulation, 16(2), 710-726, 2018
- R. Lai and H. Zhao, "Multi-scale Non-Rigid Point Cloud Registration Using Rotation-invariant Sliced-Wasserstein Distance via Laplace-Beltrami Eigenmap". SIAM Journal on Imaging Sciences, 10(2), pp. 449—483, 2017.
- R. Lai and J. Li, "Solve Partial Differential Equations on Manifolds from Incomplete Distance Information", SIAM Journal on Scientific Computing, 39(5), pp. 2231-2256, 2017.
- C. Kao, R. Lai and B. Osting,"Maximal Laplace-Beltrami Eigenvalues on Closed Riemannian Surfaces". ESAIM: Control, Optimization and Calculus of Variations, 23(2), pp. 685-720, 2017
- R. Lai and J. Lu, “Localized Density Matrix Minimization and Linear Scaling Algorithms”, 315, pp. 194–210, Journal of Computational Physcis, 2016
- V. Ozolins, R. Lai, R. Caflisch, S. Osher， “Compressed Modes for Variational Problems in Mathematics and Physics”, Proceedings of the National Academy of Sciences (PNAS), 110 (46), pp. 18368–18373, 2013.
- R. Lai and S. Osher, “A splitting method for orthogonality constrained problems”, Journal of Scientific Computing, 58(2), pp. 431–449. 2014.