**Graph Spectra and Quantum Walks** - Chris Godsil

If *A* is the adjacency matrix of a graph X, then the unitary operators
defined by
*U*(*t*) = exp(-*itA*)
define what physicists call a *continuous quantum walk*. A basic problem is to
relate the physical properties of this system to features of the underlying
graph. One important question is whether for a given graph there are distinct
vertices *a* and *b* and a time *t* such that |*U*(*t*)_{*a,b*}|=1. (If this
happens we have *perfect state transfer*.)

My talk will provide an introduction to perfect state transfer, with an emphasis on a number of connections with classical (or, at least, old) problems in graph theory.