Seminar by Zhe Sun (Tsinghua University)

Title: Rank n swapping Poisson algebras on moduli spaces

2016.05.09 | Jane Jamshidi

Date Tue 17 May
Time 15:15 16:15
Location 1530-215 (Aud. D3)


Swapping algebra, introduced by F. Labourie on pairs of points on a circle, is related to Atiyah-Bott-Goldman symplectic structure and Gelfand-Dickey second(quadratic) Poisson structure. It is restricted to rank n to relate to PSL(n, R) Hitchin component for a fixed n. Relevantly, Fock and Goncharov defined a coordinate system and a Poisson structure on their X higher Teichmuller space via affine Poisson-Lie structure, which generalize Thurston's shear coordinate and Weil-Petersson form. The main purpose of this talk is to show how the rank n swapping algebra characterizes Fock and Goncharov's language, affine Poisson-Lie structure, Poisson structure on positive grassmannian by different ways of embedding. In this way, we have a primary look at how their quantizations are related.