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Explore the intricacies of the Lightning Network in this 59-minute virtual talk presented by the Society for Industrial and Applied Mathematics. Delve into the cost analysis of Lightning Network channels and their impact on network structure with speaker Paolo Guasoni, Stokes Chair in Financial Mathematics at Dublin City University. Examine the conditions for optimal channel establishment, explicit cost formulas, and implications for network structure under cooperative scenarios. Discover how optimal network configurations avoid redundant channels, typically resulting in low-degree structures. Investigate the potential for centralization through a common intermediary when agents' payment rates are sufficiently homogeneous. Gain valuable insights into this innovative bitcoin payment protocol designed to enhance transaction speed and reduce blockchain congestion.