Abstract:Let $ Q = (Q_0,Q_1) $ be a quiver with vertices
$ Q_0 $ and arrows $ Q_1 $. A representation of $Q$ is a family of vector spaces
$ (V_i)_{i \in Q_0} $ and linear maps $ (f_{ij}) _{i\rightarrow j \in Q_1} $ between the vector
spaces.
In this talk, we will consider the category of representations of
the quiver, or, equivalently, the module category of its path algebra.
Then, we will illustrate the links between quiver representations and
two other mathematical concepts; quantum groups and cluster algebras.
