Combinatorial aspects of the representation theory of quivers.

Abstract. The first lectures will be devoted to the (generalized) Kronecker quivers and their universal coverings (the n-regular trees with bipartite orientation). The representations of the Kronecker quivers as well as the n-regular trees play an important role in many parts of mathematics. But it seems that the combinatorial constraints of Kronecker modules have not yet been understood. Afterwards, we will draw the attention to the Dynkin quivers (these are the quivers of Dynkin type A_n, D_n, E₆,, E₇, E₈). In particular, we will show that there is a strong relationship between the root posets and hammocks (as introduced by Brenner already in 1980).