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Hele-Shaw flow is a two-dimensional boundary evolution between oil and air. I will talk about two types of singularities that may occur in Hele-Shaw flow: cusps and break-offs. To describe cusps I introduce a formulation of Hele-Shaw flow in terms of minimization problem in electrostatics, and discuss a branching solution that may be related to the further evolution of cusp after its singular moment. I also describe the process of break-offs that can happen in the time-reversed Hele-Shaw flow. I will explain the universal scaling behavior and the various solutions of break-offs. Host: William Hlavacek |