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We consider a robust-optimization-driven system-level approach to interference management in a cellular broadband system operating in an interference-limited and highly dynamic regime. Here, base stations in neighboring cells (partially) coordinate their transmission schedules in an attempt to avoid simultaneous max-power transmission to their mutual cell edge. Limits on communication overhead and use of the backhaul require base station coordination to occur at a slower timescale than the customer arrival process. The central challenge is to properly structure coordination decisions at the slow timescale, as these subsequently restrict the actions of each base station until the next coordination period. Moreover, because coordination occurs at the slower timescale, the statistics of the arriving customers, e.g., the load, are typically only approximately known-thus, this coordination must be done with only approximate knowledge of statistics. We show that performance of existing approaches that assume exact knowledge of these statistics can degrade rapidly as the uncertainty in the arrival process increases. We show that a two-stage robust optimization framework is a natural way to model two-timescale decision problems. We provide tractable formulations for the base-station coordination problem and show that our formulation is robust to fluctuations (uncertainties) in the arriving load. This tolerance to load fluctuation also serves to reduce the need for frequent reoptimization across base stations, thus helping minimize the communication overhead required for system-level interference reduction. Our robust optimization formulations are flexible, allowing us to control the conservatism of the solution. Our simulations show that we can build in robustness without significant degradation of nominal performance.