Research

Research Interests

 

Online versions of my publications are available here.

I study combinatorics, graph theory and pursuit-evasion games. I am particularly interested in the interplay between randomness and strategy. For example, I have looked at controlling random walks, guiding random graph processes, playing games on random structures, and using randomized algorithms.

Along with Stan Wagon, I won the 2015 Carl B. Allendoerfer Award, a writing award given out by the Mathematical Association of America. Our article, The Sorting Hat Goes to College, describes how we use mathematical optimization to place incoming Macalester students into first-year courses at Macalester. Stan and I are currently working with a few other colleges to optimize their placements.

Teaching

Courses at Macalester

 

I have taught upper level courses in graph theory, combinatorics, optimization, network science and abstract algebra. And, of course, I teach Calculus, discrete math and linear algebra.

Please visit Moodle for all current course materials.

Here are a few Macalester news stories about some of my former honors students.

Network of Thrones

Network Science applied to Game of Thrones

 

Network Science is a new an evolving field of applied graph theory that brings together traditions from many disciplines, including sociology, economics, physics, computer science, and mathematics. The goal of network science is to understand the structure of large networks, as well as their dynamics, including how they grow and how processes evolve on networks.

For his senior capstone project, Jie Shan (Macalester 2014) and I performed a network analysis of "A Storm of Swords," the third book of George R. R. Martin's series, A Song of Ice and Fire.

We adapted our work into an article for Math Horizons Magazine, which is published by the Mathematical Association of America. Our work crossed over into the mainstream, thanks to a nice article in Quartz Magazine. You can also read more about it here.

Velvet Erdős

Velvet Erdős

 

In 2015, I fulfilled my ambition to commission a velvet painting of the incomparable Paul Erdős. Uncle Paul is an icon: he helped to define 20th century combinatorics, as a problem poser, a problem solver, and a mathematical connector. There will never be another mathematician like him.

Bruce White, a North Carolina-based artist, created a beautiful painting that now hangs in my office. Thanks, Bruce!

MAXIMA Summer REU, 2009-2014

Undergraduate Research Experience in Interdisciplinary Mathematics

From 2009 to 2014, Macalester co-hosted a Summer Math REU, along with the Institute for Mathematics and its Applications. I directed this program from 2012 to 2014. The projects came from applications in Engineering and Computer Science. In addition to the obvious mathematical reference, the moniker MAXIMA is an amalgam of the names of the hosting institutions: Macalester (or more familiarly, "Mac") and the IMA.

Each summer, 12-14 undergraduates worked in teams of four on open research problems in applied mathematics. See the MAXIMA website for more information.

MAXIMA is on hiatus for the time being. The IMA is currently on an NSF funding ramp-down. Once the future direction of the IMA has been set, we will look into rebooting the MAXIMA REU.

Here are some Macalester news stories about MAXIMA REU students.

Background

Education and Professional Experience

 
My CV

PhD, Yale University, 1997
BA, Williams College, 1991

I was Eugene Shelly Visiting Assistant Professor and Richard J. Duffin Visiting Assistant Professor in the ACO group at Carnegie Mellon University.

I spent six years working in Silicon Valley as a software engineer and architect. I worked for companies that developed platforms for supply chain management and financial services. I also worked briefly in clinical informatics.

If you want to know a little more, here are a short profile from 2011 and a stream-of-consciousness 2013 interview that appeared in the college paper, the Mac Weekly.