Teachers

Matt DeVos                    Chris Godsil
Matt DeVos Chris Godsil

Matt DeVos is a prominent discrete mathematician with significant results in a wide array of subjects, including structural graph theory, combinatorial optimization, algebraic graph theory, and additive number theory. He earned a Ph.D. from Princeton under the direction of Paul Seymour in 2000, became an assistant professor at Simon Fraser University in 2007, and recently won a Sloan Fellowship.

Chris Godsil is among the foremost researchers in the world of algebraic graph theory, and recently coauthored (with Gordon Royle) the definitive book on the subject. He is a full professor in the department of Combinatorics and Optimization at Waterloo, and he is widely known for an impressive body of research on topics such as strongly regular graphs and association schemes. More recently, Chris has turned his attention to the exciting new topic of quantum walks. This is a fascinating graph construct motivated by quantum physics, and his work here is helping to lay the foundation for this important subject.

Course

The centrepiece of this program is an intensive course in Algebraic Graph Theory. Over the first two weeks, this will feature 3 hours a day of instruction together with daily homework assignments. We wish to promote collaboration and group work, so we encourage students to work together on these problems. Furthermore, we will be introducing students to the mathematical programming language Sage, and we will use this as an educational aid. Indeed, both our instruction, and homework assignments will incoroporate this exciting tool.

Overall, the course will cover the basics of a graduate level introduction to Algebraic Graph Theory. This includes a thorough development of the theory of vertex transitive graphs, an introduction to strongly regular graphs, designs, and other importannt combinatorial structures. Additionally, we will highlight interactions between this subject and Structural Graph Theory and Additive Number Theory.

Research

During the second two weeks of the program the course load will gradually diminish and students will begin working on group research projects. Our goal will be to use Sage to aid us in the search for exceptional combinatorial structures. Although it is difficult to make significant strides in such a short period of time, there is great value in working on research problems, and our hope is that this may pave the way for future (if not present!) mathematical discoveries.

Credit

This course will be listed for credit at SFU as MATH 398. Students from external universities may be able to obtain course credit as well. Contact us for further details. Those students taking this course for credit will be given an examination during the final week.

Book

We will use Algebraic Graph Theory by Godsil and Royle. Students are encouraged to purchase the book prior to arrival.

Prerequisites

Applicants must have successfully completed a course in Linear Algebra as well as at least one course in Graph Theory and/or Abstract Algebra.