| Abstract: |
| Boundary measurement maps were first introduced by Postnikov as a tool to parametrize positroid cells in Grassmannians. They depend on the choices of a reduced plabic graph and a perfect orientation of the graph. In my dissertation, I showed that the boundary measurement maps of the top cells of Grassmannians compute the F-polynomials for DT transformations. In recent years, a new combinatorial tool called Legendrian weave was introduced by Casals and Zaslow, and it can be used to describe cluster structures on braid varieties. In this talk, I will define a new family of boundary measurement maps on Legendrian weaves, which parametrize (an open torus of) the flag moduli space in terms of weighted cycles on weaves. I will discuss how to use these boundary measurement maps to recover F-polynomials for DT transformations and their connection to the spectral networks of Gaiotto-Moore-Neitzke. This is based on joint work in progress with Yoon Jae Nho. |
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