Mathematics faculty and graduate students are invited to attend the MS Defense of Jacob McCann.

Advisor:  Dr. Maria Gillespie

Committee:  Dr. Chris Peterson, Dr. Dongzhou Huang

Title:  A LOCAL CHARACTERIZATION OF DOMINO EVACUATION-SHUFFLING

ABSTRACT: A LOCAL CHARACTERIZATION OF DOMINO EVACUATION-SHUFFLING

We consider linear intersection problems in the Grassmanian (the space of k-dimensional subspaces of C12n), 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 interpertation 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].