Explore the intersection of error correcting codes and manifold construction in this lecture by Matthew Hastings from Microsoft Research. Delve into topics such as repetition codes, quantum error correction, topology, and chain complexes. Learn about the weight of systoles, handle decomposition, and redundancy in code-based manifold building. Discover open problems in the field and gain insights into the mathematics of topological phases of matter. Recorded at IPAM's Graduate Summer School at UCLA, this talk offers a comprehensive look at cutting-edge research in quantum computing and topology.