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Like the atmosphere of Jupiter, protoplanetary disks (the flattened disks of gas and dust that orbit newly-formed protostars) are characterized by rapid rotation and intense shear, inspiring proposals that they too may be populated by massive storms analogous to the Great Red Spot. Such vortices may play a key role in the formation of planets by rapidly sweeping-up and concentrating dust particles, which may help in the formation of kilometer-size planetesimals, the "building blocks'' of planets. I study the formation and dynamics of vortices in protoplanetary disks with high-resolution, three-dimensional hydrodynamic simulations that run on parallel supercomputers, such as those found at the San Diego Supercomputer Center.