Rocky Mountain Mathematics Consortium Summer Trip

It was for the latter half of June that I had the privilege of attending the University of Wyoming's annual Rocky Mountain Mathematics Consortium (RMMC) summer program. It lasted for about a week and a half, and everyday (except for the weekends) was filled with three main lectures by notable researchers in the selected RMMC topic. Graduate students and a few professors took the time in between lectures to present contributed talks. What attracted me to the program was the topic: algebraic graph theory. On my own independent readings I had come across material discussing the relations between a graph's spectra and the properties of said graphs (e.g. graph connectivity, bipartiteness, vertex valencies...). It amazed me at those times how much you could say about a graph by looking at the eigenvalues of its adjacency matrix (it still does now!). Given this short enthusiastic blurb on graph spectra along with all of my previous graph theory posts, I'm sure my readers can imagine how incredibly stoked I was when I received word of acceptance to the conference/program.

The three lecturers for RMMC were Chris Godsil of the University of Waterloo, William Martin of Worcester Polytechnic University, and Joanna Ellis-Monaghan of Saint Michael's College. Their lectures covered material on quantum graph walks, coding theory, and graph polynomials respectively. I purchased a notebook before my trip to Wyoming expecting that I had more than enough paper for RMMC, but at the end of it all I had a notebook completely stuffed with graph theory ideas; not an inch of white space to spare! Among the topics discussed (both from lectures and from contributed talks) were the following (and do note that this is only a small sample listing; the list goes on and on and on!): edge deletions and contractions, the Tutte polynomial, strongly regular graphs, Hamiltonian cycle detection, graph energy, the spectral decomposition of graphs, Hadamard matrices, n-cube graphs, graph toughness (this was actually discussed the Sunday before the program actually started), linear programming methods for the social networking influence maximization problem, eigenvalues of directed graphs, and some knot theory basics. Phew! :-0 To review the daily material presented in main lectures, we also had a problem solving session at the end of every other day. During these problem solving sessions we could ask the lecturers questions about the problems they made up and collaborate with other students on them.

Among the many graduate students I met at the conference, there were two I spent many of my problem solving sessions with and got to be great friends with. Pictured below are the three of us. That is of course me in the middle, and to my left and right are Saba and Danielle. 

The picture setting was a banquet that RMMC held for all of us during the last week we were there (hence the fancy glasses and table cloths). It was a great dinner and a time to take lots of pictures and relax after all of the hard studying and work. RMMC was a great experience and it is very possible that I will discuss it or at least some of the topics presented there more in future posts. :-)