Volkmar Welker: On the ideal of orthogonal representations of a graph

Abstract

Orthogonal representations of a graph were introduced by Lovasz in
the late 70s. An orthogonal representation of a graph G in real d-space is
a map that send each vertex to a vector such that two vertices not
joined by an edge are mapped to vectors that are orthogonal with respect to
the standard scalar product. Lovasz, Saks and Schrijver later studied the
semialgebraic set of all (generic) orthogonal representations.
Together with Herzog, Macchia and Madani we studied algebraic properties
of the ideal of equations defining the orthogonality relations.
In the talk I will present our results together with background information
on orthogonal representations.