Tobias Müller CWI Amsterdam, the Netherlands Some results on geometric representations of graphs A d-dot product representation of a graph G assigns a vector u_i in R^d to each vertex i, in such a way that u_i^T u_j >= 1 if and only if {i,j} is an edge of G. The least dimension d for which such a representation exists is called the dot-product dimension of G. By making use of some classical results in algebraic geometry, oriented matroids and the Colin de Verdiere graph parameter, I will sketch the proofs of some results on dot product representations and other geometric representations of graphs. (based on joint work with Ross Kang)