The course will discuss recent advances of theories and numerical algorithms utilizing tensor decompositions to reduce the computational costs of numerically solving partial differential equations, especially recent advances for kinetic equations. The course will discuss basic ideas of tensor-decomposition, iterative linear solvers for tensor equations and related low-rank preconditioners, time marching techniques based n Dynamical simulations for kinetic equations, quantum physics, chemistry and uncertainty quantification. Students should seek the course instructor’s approval to take this course.