Algebraic Graph Theory Seminar - Emily King

Title: Switching Equivalence on the Grassmannian

Abstract:

When constructing configurations of subspaces with desirable properties, one might ask if the configuration is indeed "new.''  It has been known for about 50 years that Gram matrices of equiangular vectors in real Euclidean space correspond to finite simple graphs via the Seidel adjacency matrix, and the collections of such vectors which span the same lines correspond to switching equivalence classes of graphs.  In this talk, known generalizations of this correspondence to complex vectors will be leveraged to show hidden combinatorial structures in nice vector configurations.  Further, new invariants to show "switching equivalence'' of subspaces which have dimension greater than 1 (i.e., points on the Grassmannian) will be presented.