Heisenberg calculus and cyclic cohomology

On a compact contact manifold, a pseudodifferential operator in the Heisenberg calculus with an invertible symbol is a hypoelliptic Fredholm operator. In this talk I will discuss solution of the problem of finding a local formula for the index of such an operator as an expression in terms of the principal symbol of the operator and geometric data. This is a joint work with E. van Erp.