This talk will review the active area of aggregation equations - problems in which material is advected by a flow field resulting from nonlocal interactions of the material. Such equations arise in many applications including biological swarming models, material science applications, and superfluids. Many recent results on such problems came out of or were inspired by IPAM's ``Optimal Transport'' program.
I will discuss connections between these problems and famous problems in fluid mechanics including the Clay Math Prize problem and classical modeling problems connecting molecular dynamics to continuum limits.
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