I have been at WPI for a long time. It’s been exciting to participate in the evolution of the Institute and to adapt to changes along the way. As a mathematician, my focus is graph theory, a relatively new area of mathematics that was not offered when I was a student. Today, graph theory enjoys a lot of attention with over a dozen journals devoted to it and with applications to many fields within and outside of mathematics. In particular, computer scientists and electrical engineers make good use of graph theory and have contributed to its growth. Perhaps I should explain that the term “graph” here does not refer to a function like sine x, but to a network of points and lines. One might wonder what types of questions arise in the study of such structures. Consider, for a simple example, the problem of determining the shortest route for a driver delivering goods to a number of cities. Graph theory is a branch of discrete mathematics that has close ties with many other areas of mathematics. I am interested in all aspects of graph theory, including symmetry of graphs (group theory), extremal problems (combinatorics), and eigenvalues (matrix algebra). At WPI student interest in graph theory has grown tremendously. I particularly enjoy working with students on graph theory research projects.
Mathematicians say that the easier it is to state a claim, the more difficult it is to prove it. For example, an efficient algorithm for delivering goods to cities has not been found. I tend to gravitate toward trying to solve some easily stated claims. However, when working with students, I choose research problems that are current and accessible to them, meaning that there is a good chance of obtaining results. Getting answers is sometime a matter of asking the right questions.