Explore innovative computational approaches for solving high-dimensional partial differential equations (PDEs) in this 53-minute lecture presented by Yuehaw Khoo from the University of Chicago at IPAM's Tensor Networks Workshop. Delve into the application of tensor networks and convex relaxations to construct inner and outer approximations of PDE solutions using low-order statistics. Discover how these techniques effectively combat the curse of dimensionality, offering new perspectives on tackling complex mathematical challenges in high-dimensional spaces.