[Test graduate students' ability to analyze convergence and robustness of decentralized federated optimization algorithms operating under statistical heterogeneity (non‑IID data), intermittent connectivity (time‑varying or lossy networks), and Byzantine participants. Assess understanding of modeling assumptions (mixing matrices, spectral gap, adversary models), proving convergence rates or identifying divergence conditions for methods such as decentralized SGD, local SGD, and gossip-based protocols, and designing/justifying Byzantine‑resilient and communication‑robust mechanisms (robust aggregation, redundancy, coding, compression). Tasks may include deriving convergence bounds, characterizing trade‑offs between communication and robustness, proposing mitigation strategies, and critiquing theoretical and empirical evaluations.]