4:30 pm Thursday, March 5, 2015
Geometry Seminar: Laminations from the symplectic double by Dylan Alegretti (Yale) in RLM 9.166
As part of their work on quantization of cluster varieties, Fock and Goncharov introduced an algebraic variety called the symplectic double. Building on my pre-talk, I will describe two new constructions in geometry which are closely related to this variety. The first is a modified version of the Teichm\"uller space of a doubled surface, and the second is a version of the space of measured laminations. The modified Teichm\"uller space is identified with the set of positive real points of the symplectic double, while the space of laminations is identified with the set of tropical points. There is a canonical pairing between the Teichm\"uller and lamination spaces, and I will describe an explicit formula for this pairing using the F-polynomials of Fomin and Zelevinsky. Submitted by
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