This lecture is an introduction to the interesting phenomena of nonlocal aggregation equations and to the open problems in this area. I will review numerical and analytical results for both kinematic and dynamic aggregation equations. I will discuss how models are constructed and the emergence of phenomenological behavior for different types of models including flocking, milling, and other patterns. I will also review some results on well-posedness of aggregation equations including a sharp condition on blowup from smooth initial data. I will talk about connections between these results and classical fluids problems including vortex patches and vortex sheets.
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