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Learn about the intersection of probabilistically checkable proofs (PCPs) and fault-tolerant routing through high-dimensional expanders (HDX) in this 53-minute conference talk. Explore how HDX structures can be leveraged to construct size-efficient PCPs while simultaneously addressing challenges in fault-tolerant network routing. Discover the mathematical foundations connecting these seemingly disparate areas of theoretical computer science and understand the practical implications for both proof systems and network reliability. Examine the technical approaches used to achieve efficiency improvements in PCP construction and how the same underlying principles apply to creating robust routing protocols that can handle network failures.
