Modified traces on quantum sl(2) and logarithmic invariants

In this talk I will discuss a link invariant arising from the restricted quantum of $sl(2)$ at a $2p$-th root of unity. In particular, I will show how we can use a modified trace on the quantum group itself to define a Logarithmic invariant of colored links. Using the integer on the quantum group, this invariant can be extend to an invariant of colored links in a 3-manifold. We expect this 3-manifold invariant to lead to a TQFT. This is joint work with Anna Beliakova and Christian Blanchet.