Dynamical systems applied to physics, biology, and social science.
I have broad interests in applied mathematics. At the beginning of my career I was fascinated by mathematical biology and worked on a variety of problems, including the geometry of supercoiled DNA, the dynamics of the human sleep-wake cycle, the topology of three-dimensional chemical waves, and the collective behavior of biological oscillators, such as swarms of synchronously flashing fireflies. In the 1990’s, my work focused on nonlinear dynamics and chaos applied to physics, engineering, and biology. Several of these projects dealt with coupled oscillators, such as lasers, superconducting Josephson junctions, and crickets that chirp in unison. In each case, the research involved close collaborations with experimentalists. I also love branching out into new areas, often with students taking the lead. In the past few years, this has led us into such topics as: mathematical explorations of the small-world phenomenon in social networks (popularly known as “six degrees of separation”), and its generalization to other complex networks in nature and technology; the role of crowd synchronization in the wobbling of London’s Millennium Bridge on its opening day; and the dynamics of structural balance in social systems.
I’m also passionate about communicating mathematics to the public. For example, I wrote a weekly column on mathematics for the New York Times in the spring of 2010 and the fall of 2012. My most recent books, The Joy of x and Infinite Powers, are aimed at general readers curious about our beautiful subject. And my podcast for Quanta Magazine, called The Joy of Why, takes listeners into some of the biggest unanswered questions in math and science today.
- Infinite Powers: How Calculus Reveals the Secrets of the Universe, Houghton Mifflin Harcourt, 2019.
- Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, 2nd edition, Westview Press, 2014.
- Collective dynamics of 'small-world' networks (with D. J. Watts), Nature 393 (1998), 440–442.
- Sync: The Emerging Science of Spontaneous Order, Hyperion, 2003.
- Synchronization of pulse-coupled biological oscillators (with R. E. Mirollo), SIAM Journal on Applied Mathematics 50, 1645-1662 (1990).
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