Degenerations of skein algebras and pants decomposition

For a surface with an ideal triangulation, Bonahon and Wong showed that the skein algebra of the surface can be embedded into a quantum torus, where a quantum torus is a non-commutative algebra with nice properties. However, the case of closed surfaces is still open since their proof used an ideal triangulation essentially and any closed surfaces have no ideal triangulations. In this talk, we give an embedding of a “degeneration” of the skein algebra of a closed surface into a quantum torus. This is joint work with Thang T. Q. Le (Georgia Institute of Technology).