# Quantum hyperbolic 6j-symbols

## Francis Bonahon

Traditionally, a 6j-symbol is a certain algebraic machinery associated to a combinatorial tetrahedron with various representations attached to its faces, edges or vertices. Combining the 6j-symbols associated to the simplices of a manifold then defines an invariant of this manifold. One example is the Kashaev 6j-symbol, defined by considering the representation theory of the Weyl Hopf algebra. We will introduce a more geometric discussion of this Kashaev 6j-symbol. In particular, it is closely connected to the geometry of ideal tetrahedra in hyperbolic 3-space.

This talk will be accessible to graduate students.