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Browsing by Author "McCann, Jacob, author"

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    A local characterization of domino evacuation-shuffling
    (Colorado State University. Libraries, 2024) McCann, Jacob, author; Gillespie, Maria, advisor; Peterson, Christopher, committee member; Huang, Dongzhou, committee member
    We consider linear intersection problems in the Grassmanian (the space of k-dimensional subspaces of Cn), where the dimension of the intersection is 2. These spaces are called Schubert surfaces. We build of the previous work of Speyer [1] and Gillespie and Levinson [2]. Speyer showed there is a combinatorial interpretation for what happens to fibers of Schubert intersections above a "wall crossing", where marked points corresponding to the coordinates of partitions coincide. Building off Speyer's work, Levinson showed there is a combinatorial operation associated with the monodromy operator on Schubert curves, involving rectification, promotion, and shuffling of Littlewood-Richardson Young Tableaux, which overall is christened evacuation-shuffling. Gillespie and Levinson [2] further developed a localization of the evacuation-shuffling algorithm for Schubert curves. We fully develop a local description of the monodromy operator on certain classes of curves embedded inside Schubert surfaces [3].