**abstract:**
We show that specializations of the homological representationsof braid
groups are equivalent to the monodromy of the KZ equation with values in the space of null vectors in the tensor product of Verma modules when
the parameters are generic. Here the representations of the
solutions of the KZ equation by hypergeometric integrals due to
Schechtman, Varchenko and others play an important role.
By this construction we recover quantum symmetry of the
monodromy of KZ connection due to Drinfel'd and myself by
means of the action of the quantum groups on twisted cycles.
In the case of special parameters corresponding to conformal
field theory, we give a description of twisted cycles.

Tue 17 Feb, 9:30 - 10:10, Aula Dini

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