Algebraic Combinatorics: Spectral Graph Theory, Erdös-Ko-Rado Theorems and Quantum Information Theory

Monday, June 23, 2014 12:00 am - Friday, June 27, 2014 12:00 am EDT

A conference to celebrate the work of Chris Godsil

It is surprising that the characteristic polynomial of

Chris Godsil
the adjacency matrix of a graph provides a useful window onto combinatorial properties of the graph itself, but this approach to graph theory has been a source of interesting and useful results for over 80 years.

Questions on optimality of networks and extremal graph theory lead to a huge literature on distance-regular graphs and association schemes, with applications to finite geometry, coding theory, and the theory of finite simple groups. Work on the matching polynomial, an analogue of the characteristic polynomial first studied by chemists and physicists, led to the best asymptotic estimates for the number of k × n Latin rectangles. Wilson used association schemes in his fundamental work on the Erdös-Ko-Rado theorem, a central result in extremal graph theory, and more recent work has shown algebraic approaches to this topic provide a very useful viewpoint.

More recently, it has become apparent that many questions on quantum information theory give rise to problems which can be fruitfully attacked using the methods and ideas of algebraic graph theory: existence of mutually unbiased bases, SIC-POVMs, quantum colouring and homomorphisms, discrete and continuous quantum walks.

Professor Chris Godsil has made many fundamental contributions to these topics. The goal of this conference is to bring together researchers in discrete mathematics whose work has been influenced by Chris's work, to share recent advances, and to forge stronger connections. The conference will be a celebration for the Canadian mathematical community and we invite researchers in combinatorics, matrix theory, and quantum information theory from all over the world to join us.