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Title: Fault Tolerant Routing and High Dimensional Expanders

Abstract: We will go over some recent results about fault tolerant routing from Bafna, Minzer, Vyas. Two parallel series of works from the last few years from Bafna, Lifshitz, Minzer, Vyas as well as Dikstein, Dinur, Lubotzky has led to size efficient PCPs by using high dimensional expanders. We will comment on the context for these works, and briefly go over some high level ideas. Then, we will talk about an application to fault tolerant rounding. The goal in this problem is to design a sparse network supporting efficient fault tolerant interactions between all pairs of nodes. Using the size efficient PCP construction, Bafna and Minzer gave a construction of constant degree networks with efficient protocols that tolerate a constant fraction of adversarial edge faults.