Title: Triangulations and Soliton Graphs for the totally positive Grassmannian
Speaker: Rachel Karpman (Ohio State University)
Abstract: The KP equation is a nonlinear dispersive wave equation which gives an excellent model for resonant interactions of shallow-water waves. Regular soliton solutions of the KP equation may be constructed from points in the totally nonnegative Grassmannian of N-planes in M-dimensional space. For the positive Grassmannian of 2-planes in M-space, Kodama and Williams showed that soliton graphs are in bijection with triangulations of the M-gon. We extend this result to Gr(N,M) when N = 3 and M = 6, 7, or 8. In each case, we show that soliton graphs are in bijection with Postnikov's plabic graphs, which play a key role in the combinatorial theory of the positive Grassmannian.
Seminar URL: https://research.math.osu.edu/gcis/
