### Kashaev coordinates on Teichmuller space

#### Xiaobo Liu, Columbia University

Abstract: Kashaev introduced a new set of coordinates on
the Teichmuller space of a punctured surface. We will discuss
the relation between Kashaev coordinates and the conventional
coordinates, Penner coordinates and shear coordinates.
On the other hand, in Kashaev's original volume conjecture,
the special value of the colored Jones polynomial took the
form of a state sum constructed from the 6j-symbol
of the Weyl algebra. We will explain how an algebraic formalism of
quantum Teichmuller space in Kashaev coordinates
(local representations) leads Hua Bai to identify Kashaev's
6j symbol in quantum Teichmuller theory.