Description
We shall consider free groups of arbitrary finite, even rank, and their quotient by one relator leading to surface groups. The aim of the talk is to present different families of traces on the free group, that interpolate between the regular trace on the quotient and the regular trace on the free group, while being motivated by matrix approximations. When the rank is 2, the non-commutative distribution of the generators of the free group interpolates between freely independent and classically independent Haar unitaries.
