Title: Graphs, Polytopes, Quadrics

Abstract: Let $X$ be a graph with adjacency matrix $A$ and eigenvalue $\theta$. The projections of the 
standard basis vectors onto the $\theta$-eigenspace of A generate a convex polytope, and properties 
of this polytope relate in an interesting way to properties of X. We can use knowledge of the 
facets to derive the Erd\H{o}s-Ko-Rado theorem. We can also use information about the real quadrics 
that contain the vertices of the polytope to constrain the structure of X. In my talk I will 
explain these connections. 