| Abstract: |
| An open positroid variety is a geometric object appearing in Postnikov`s stratification of the totally non-negative Grassmannian, and a result of Galashin and Lam is that the homogeneous coordinate ring of such a variety has two natural cluster algebra structures. Muller and Speyer conjectured a precise relationship (quasi-coincidence) between these two cluster structures, implying in particular that they define the same positive part of the variety. In this talk, I will explain how to understand the cluster structures and prove Muller and Speyer`s conjecture using the techniques of additive categorification. |
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