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The objects of interest in this thesis are positroid varieties in theGrassmannian, which are indexed by juggling patterns. In particular, we studyaffine patches on these positroid varieties. Our main result corresponds theseaffine patches to Kazhdan-Lusztig varieties in the affine Grassmannian. Wedevelop a new term order and study how these spaces are related to subwordcomplexes and Stanley-Reisner ideals. We define an extension of pipe dreams tothe affine case and conclude by showing how our affine pipe dreams aregeneralizations of Cauchon and Le diagrams.

Affine Patches on Positroid Varieties and Affine Pipe Dreams (Thesis)