Monday, June 17
Mudd Hall Auditorium
Chair: Leslie Hall, The Johns Hopkins University
The speaker will present a survey of several recent developments concerning Colin de Verdiere's invariant. In particular, he will discuss a surprising connection with a classical theorem of Koebe on representations of planar graphs by touching circles, and a theorem of Cauchy on the rigidity of convex polytopes in 3-space, and use this connection to characterize the cases when mu is close to n, the number of nodes. This leads to the study of representations of graphs that generalize Koebe's construction (representations by orthogonal circles, for example). We also describe a key lemma of Van der Holst, and show how it leads to a number of interesting related linear algebraic invariants, introduced by Van der Holst, Schrijver and Laurent, and others.
Department of Computer Science