Explore the future of exascale computing architectures in this comprehensive lecture presented by Erik Draeger from Lawrence Livermore National Laboratory. Delivered as part of IPAM's New Mathematics for the Exascale: Applications to Materials Science Tutorials at UCLA, this 70-minute talk delves into the cutting-edge developments shaping the next generation of supercomputers. Gain insights into the challenges and opportunities presented by exascale computing, with a particular focus on its applications in materials science. Discover how advanced mathematical techniques are being developed to harness the power of these upcoming architectures, potentially revolutionizing scientific research and computational capabilities.