**Monodromy representations of braid groups**

The group *B*_{n} of braids on *n* strands is the fundamental
group of the
configuration space of *n* points in the plane. Thus, by considering
some fiber
bundle over the configuration space and taking the corresponding monodromy
homomorphism, one obtains a representation of *B*_{n}.
In this talk we discuss the
following representations, treating each of them as a monodromy homomorphism:

- Artin representation.
- Burau representation.
- Lawrence-Krammer-Bigelow
representation (a faithful linear representation of
*B*_{n}, by a recent result)
and, if the time permits,
- Chen's iterated integral of a canonical formal
power series connection, which is the same thing as Kontsevich integral for
braids.

*Ivan Izmestiev*

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