JOINT COLLOQUIUM
DEPARTMENT OF MATHEMATICS
& DEPARTMENT OF COMPUTER SCIENCE
CLARKSON UNIVERSITY
THURSDAY AUGUST 3 2023. 11:00. SCIENCE CENTER 356
CHRIS GODSIL
Department of Combinatorics and Optimization
University of Waterloo
CONTINUOUS QUANTUM WALKS ON INFINITE GRAPHS
A continuous quantum walk on a graph X with adjacency operator A is determined by the 1-parameter family of unitary operators U(t) := exp(itA) (for real t). We have perfect state transfer from vertex a to vertex b at time t if jU(t)a;bj = 1, and the vertex a is periodic if there is a positive time t such that jU(t)a;aj = 1. If there is perfect state transfer from a to b at time t, the vertices a and b are each periodic at time 2t. For nite graphs, we have extensive theory about the occurrence of perfect
state transfer and periodicity. I will discuss some of the ideas and tools in a recent proof that connected in nite graphs with bounded valency do not have periodic vertices.
Biographical Sketch: Chris Godsil received his B.Sc. degree in Biochemistry and
Ph.D. in Mathematics from the University of Melbourne. He had spent some time
at Syracuse University and also at Montanuniversitat at Leoben in Austria. He
was a faculty member at Simon Fraser University before joining the Department of
Combinatorics and Optimization at the University ofWaterloo in 1987. His research
interests are in algebraic graph theory and combinatorics. He has co-authored two
of the standard textbooks on the topic: \Algebraic Combinatorics” and \Algebraic
Graph Theory” (with G. Royle). His recent books include the research monographs
on the Erdos-Ko-Rado theorems (with K. Meagher) and discrete-time quantum
walks (with H. Zhan). He is a founding member of the Journal of Algebraic Com-
binatorics. In recent years, he has pioneered the use of techniques from algebraic
graph theory to study fundamental questions in quantum information theory.
Contact: Mathematics and Computer Science, Clarkson University, 268-2395
