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Positroid varieties are subvarieties in the Grassmannian defined by
cyclic rank conditions and which are related to Schubert
varieties. They are also connected to N=4 supersymmetric Yang-Mills
theory. In this talk, we will discuss recent work by the author
studying whether torus-fixed points on positroid varieties are
smooth. This will involve looking at combinatorial diagrams called
"affine pipe dreams."