The program "Algebraic Graph Theory" will run from June 17-28, 2013, at the University of Wyoming. This summer school is part of an annual program sponsored by the Rocky Mountain Mathematics Consortium (RMMC). The purpose of this program is to introduce graduate students and researchers to topics in algebraic graph theory and their applications, foster collaboration, and build ties between young researchers. Daily lectures will provide the participants with background in the subject, and contributed talks and problem sessions in the afternoon will reinforce the lectures and give the participants a chance to work together on open problems.
The use of algebraic techniques to solve graph theory problems has been a very fruitful approach, and continues to have applications beyond pure mathematics to physics, computer science, biology and statistics. The topics covered include spectral graph theory with applications to quantum computing, association schemes with applications to design and coding theory, and graph polynomials with applications to the Potts model and DNA self-assembly. The aim is for a diverse body of student and researchers. Participation of members of groups underrepresented in mathematics is encouraged and supported.
More information about the program can be found at:
www.uwyo.edu/jwilliford/rmmc2013/rmmc_2013.html
," which was held on the University of Wyoming campus during June 17th-28th. There were 64 total participants representing universities from 22 different states in the USA, with a handful of international participants representing six different countries. The participants were largely graduate students, including female students and minorities. NSF grant funds were used to offer housing, cafeteria meals and partial travel to many participants. Scientific Program: There were three main speakers at the workshop, each of which gave a series of 10 lectures on algebraic graph theory and its applications. We list the speakers and topics below: Chris Godsil, University of Waterloo Topics: discrete and continuous quantum walks, quantum approaches to graph isomorphism, using sage for algebraic graph theory William J. Martin, Worcester Polytechnic Institute Topics: codes, designs, association schemes and bounds for combinatorial objects Joanna Ellis-Monaghan, Saint Michael’s College Topics: graph polynomials, graph theory applications in DNA self-assembly In addition to these lectures, there were 22 contributed talks by participants on a wide range of topics in algebraic graph theory and combinatorics. There were evening problem sessions for the 10 weekdays of the workshop during which participants would work on exercises and open problems related to the lectures. The full schedule can be found at the conference website: www.uwyo.edu/jwilliford/rmmc2013/rmmc_2013.html Social Program: The goal of the social program was to create an environment of comradery among speakers and participants alike to build ties and lead to a free exchange of ideas. To this end, was a picnic and banquet for all attendees, and weekend hikes organized by Diane Wagner. In addition to these scheduled activities, the majority of participants all resided and dined in the same hall and cafeteria. The principal speakers also ate at this cafeteria with the other participants. This allowed for more interaction/mentoring outside of the daily program. Reaction: Reactions of the participants were gauged by two surveys, one given at the end of the program and the other given a year later. The results were very positive overall, with most participants describing the content of the lectures as excellent. Many indicated that they made lasting connections with other participants. Some of these connections have led to collaborative work. Most notably, new examples of perfect state transfer in distance-regular graphs were discovered during the workshop. Intellectual Merit and Broader Impacts: The program brought topics in algebraic graph theory to a diverse audience, and gave examples of applications that are interdisciplinary in nature. This workshop has the potential to spur transformative research in the area of algebraic graph theory by stimulating interest in its applications to physics, computer science and biology. The gathering also gave opportunities for mentoring and networking critical for students and researchers at smaller or more isolated institutions. The diverse collection of participants benefited all by providing a more heterogeneous working environment. The contributed talks offered students and other researchers the opportunity to share their ideas with a broad audience. The majority of the participants are destined to become professors. The series of lectures given by the main speakers, which were overall reviewed as excellent and well organized, will likely provide a strong influence on how the participants design their own lectures. Links to material from the lectures are available on the conference website so that anyone interested can benefit.
