COSAM News Articles 2021 February Interview with Chris Rodger

# Interview with Chris Rodger

Published: 02/02/2021

By: Luke Oeding

Chris Rodger, who retired from the Department of Mathematics and Statistics is now an Emeritus Professor, (virtually) sat down with Luke Oeding to learn more about his career and plans for the future.

Q: What was your trajectory [where you grew up, where you studied, and what other places you worked] that brought you to Auburn?

Q: What is your favorite Mathematical Theorem (and why)?

Vizing’s Theorem, for sure! It states that the minimum number of colors needed to properly color the edges of a simple graph is either the maximum degree, Δ, of the graph, or is Δ+1. So why is Vizing’s Theorem my favorite? First, it has many really interesting extensions and generalizations. For example, is the answer Δ or is it Δ +1 (this is an NP complete decision) and are there interesting conditions on the graph which would mean that you know for sure which it is?  But foremost for me was because it and its generalizations enabled me to help in the introduction of graph coloring as a technique to answer open questions in Combinatorial Designs. One of those was a question posed in the early 1970s by Curt, which I, with Tony Hilton and Lars Andersen, solved in my PhD dissertation in 1982: can a partial idempotent latin square of order n always be embedded in an idempotent latin square of order t, for all t ≥ 2n+1? I recall nervously visiting the Department of Combinatorics and Optimization at the University of Waterloo in Canada, the mecca for research in Combinatorics at the time, giving a talk on this method, and being told by Adrian Bondy (he and U. S. R. Murty wrote one of the two best books on graph theory) that it was the first time he had heard a talk that meaningfully used graph theory in a design theory setting. That was really affirming for a young aspiring researcher! More recently, the edge-coloring approach has been critical in developing amalgamations to settle some neat graph and hypergraph decomposition problems.

Q: What's your favorite experience teaching Math?

There are so many, but if there is a unifying feature it would be changing people’s attitudes towards math. I have spent a lot of the second half of my career working with teachers across Alabama, some of whom really feared mathematics, yet had to teach it. But in a nurturing environment it was so rewarding to see them go from tears to elation by challenging them mathematically and gently prodding their thought processes to success. I vividly recall regularly driving over to west Alabama wondering why I was going, then driving back in the glow of the teachers’ appreciation and excitement as they mastered problem solving scenarios. This also happens in undergraduate classes, especially our core curriculum Discrete Math class, and even with graduate students as they overcome hurdles, sometimes phoning me with the need to share the joy of a sudden breakthrough in their dissertation research.

Q: Which of your research results are you most proud?

The answer here is more about developing a technique, namely amalgamations and associated disentanglements of graphs, which led to my favorite results concerning partitioning the edges of families of graphs so that the graph induced by each element in the partition is an interesting graph in its own right. Hamilton decompositions and Steiner triple systems both fall into this category. It is especially powerful in obtaining embedding results that were previously well beyond the reach of researchers. In particular, such embedding results can be used to solve some scheduling problems where pre-set conditions must be met. For example, think of an extension of the famous traveling salesman problem. The salesman goes out several times each month, being required to visit each big town on every trip, but visiting the smaller towns once a month. The mathematical model would represent each big town with a vertex (i.e., a dot, like on a map), adding edges to represent roads joining big towns which contain some of the small towns. Each trip requires selecting some edges (roads to drive along) so that each vertex (big town) is included exactly once; this is called a Hamilton cycle in the graph, named after a famous 19th century mathematician who developed a game using this kind of problem. So the aim is to find several Hamilton cycles, one for each trip, so that each edge is used in exactly one of the chosen Hamilton cycles. The preset conditions would be of the type that says on a trip where I go along this road, I want to include these roads too. Visually, you can describe one trip by coloring the chosen edges (roads) used with the same color. So the preset condition requires some chosen edges to already be colored. In particular, an embedding might prescribe the color of each edge joining two vertices in a chosen subset of the vertices (maybe all the edges joining “big” towns near Montgomery come pre-colored). Then all remaining edges need to be colored in the embedding process so that in the end each color describes a Hamilton cycle. Roughly speaking, to do this, the amalgamation method would combine all the unchosen vertices into a single vertex, all its incident edges would be then be colored, and finally single vertices would be disentangled one by one from the single vertex to form the required schedule. Mathematicians reading this can think of the method as disentangling the effects of an envisaged homomorphism to create the object one has in mind. The starting graph, the coloring of its edges and loops, and the untangling process itself have to be chosen carefully.

Q: Among your many accomplishments at Auburn, of which are you most fond?

I often think about my 32 PhD students (soon to be 34), with many of whom I still have contact. They have gone on to successful careers in academia and industry, and I think of my time with them fondly. Their careers include outstanding researchers in academia, great teachers at universities and colleges, administrators from chairs to Deans to Vice-Presidential levels, and analysts working in industry in high tech and actuarial positions. So I am very happy for them! Meeting with them was a delight, not only for the excitement generated by their research, but also just for the interpersonal interactions.

Q: Tell us a little bit about the outreach programs you’ve been involved in and their impact on the state and region.

I am proud of my outreach efforts with teachers across the state, for which I received the Auburn University Outreach Award. That enabled me to jump into helping outreach at Auburn receive a higher standing, even being a primary activity for earning tenure. For the first half of my career I was very focused on my research. In the late 1990s, Rutgers had a wonderful program funded by the NSF that gave month-long on-site research experiences for high school teachers, the first week of which was held at the same time as a conference for researchers. I was one of those researchers one year, then returned the next year to actually organize the research week. This interaction with teachers (we stayed at the same hotel and would challenge them with problems at night), together with visiting another program held there for elementary teachers, exposed me to active learning situations and good ways to involve teachers in mathematics. I tried to get Alabama teachers to attend, but finally, with Rutgers faculty, we got the NSF to fund a site at Auburn. Teachers came from many counties, but most were from Lowndes County and they loved the experience so much that they invited me to run the 10 day program in Mosses, Alabama. From there we spread westwards, returning to Selma for 3 subsequent years, having found funding from private foundations and the Alabama Council for Higher Education. Logistically it was a challenge, even just to get food for them for lunch when we were at Mosses, since Lowndes County is one of the poorest in the USA. The teachers throughout were fantastic, and really bought in to the program. I thought I was going there to help them with content acquisition, which was one factor. But I quickly realized that the problem solving setting addressed a more serious problem, namely having confidence in their ability to understand and do mathematics. Anecdotally, one teacher confided in me when returning to run follow-ups during the subsequent year that they used to extend the morning break so that less time was left to teach math when the kids returned; but now that teacher spends the full amount of time allocated for math! It was a time when the No Child Left Behind Program mandated that teachers be “highly qualified”, so helping some achieve that bar ended up being another successful effort. This activity blossomed into being awarded a massive NSF grant of over \$9 million with 3 other Principle Investigators (Phil Zenor being one and two others in Math Ed, Strutchens and Martin; with Steve Stuckwisch playing a vital role too). We worked with around 2000 teachers throughout East Alabama, most interacting with us for over 100 hours. My role was mainly focused on math content that stretched the teachers, giving them a richer environment to understand the math they were expected to teach. It was really a great extension to my career.

Q: What is the best part of an academic career?

Q: Any advice for a young mathematician / statistician?

Ask questions! When you are listening to a mathematics talk, ask yourself questions like “What related questions might be worth studying?” and “Are any of the techniques used applicable to my research?” When you read research papers, do it actively by asking yourself “How would I go about proving that result?” before you start, and throughout the proofs ask “What would I do next?” Asking good research questions is one of the last skills I see develop in graduate students, but having a successful research career can depend on honing that skill.

Q: What do you want to do when you grow up (AKA Retire)?

COVID has certainly changed the immediate look of my retirement. My wife, Sue, and I have done many walks in state and national parks over the past 9 months, and that has been fantastic. I will return to playing my violin the Montgomery Symphony and the Auburn Community Orchestras once it is safe to be close to people blowing instruments! And my church choir is in the same boat, but will be a big part of my life again soon. We have been invited to sing with the Mormon Tabernacle Choir next summer, and sang with Heather Sorenson in Carnegie Hall last year. I enjoy playing tennis, even through the current COVID pandemic, and I will return to umpiring NCAA tennis in the spring. I am on the ITA’s (Intercollegiate Tennis Association) national executive committee, chairing the Rules Committee that oversees all NCAA tennis officiating. I continue to be the treasurer of the Food Bank of East Alabama. Reading and gardening are also things I enjoy. But keeping up with family is top of the list!

Q: If I might be so bold to ask, what do you hope will be your legacy?

It’s ok for math faculty to take teaching seriously. I have been fortunate to have had many successes and recognition for my research, but throughout my career teaching has always been important to me. Institutionally, that was unusual when I began my career, in that tenure and other rewards were typically associated with research. But I have dabbled with, and then immersed myself in, mathematical educational situations where I could make a difference by using my depth of knowledge as a researcher coupled with my interest in how to pass along technical information to less experienced people. I think my involvement is helping this become an acceptable pursuit in the mathematical academic community. Being a PI on two large NSF grants and multiple smaller grants didn’t hurt either!