Coordinate Methods for Solving Eigenvalue Problems in High Dimensions
The leading eigenvalue problem of a differential operator arises in many scientific and engineering applications, in particular quantum many-body problems. Due to the curse of dimensionality conventional algorithms become impractical due to the huge computational and memory complexity. In this talk, we will discuss some of our recent works on developing efficient coordinate based approaches for eigenvalue problems in high dimension and on convergence analysis of randomized coordinate algorithms based on the theory of random dynamical systems. (joint work with Ziang Chen, Yingzhou Li, and Zhe Wang)
Jianfeng Lu is a Professor of Mathematics, Physics, and Chemistry at Duke University. Before joining Duke University, he obtained his PhD in Applied Mathematics from Princeton University in 2009 and was a Courant Instructor at New York University from 2009 to 2012. He works on mathematical analysis and algorithm development for problems and challenges arising from computational physics, theoretical chemistry, materials science, high-dimensional PDEs, and machine learning. His work has been recognized by a Sloan Fellowship, a NSF Career Award, and the 2017 IMA Prize in Mathematics and its Applications.