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EducationPh.D. (1986) Harvard University Research Area: Applied MathematicsI 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 parametric resonance in microelectromechanical systems (MEMS); the nonlinear dynamics of HIV interacting with the immune system; and mathematical explorations of the small-world phenomenon in social networks (popularly known as "six degrees of separation"). Currently, we have been studying a wide variety of complex networks in both the natural and social sciences, using ideas from graph theory, statistical physics, and nonlinear dynamics. Selected PublicationsNonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, Perseus Books, 1994. Synchronization transitions in a disordered Josephson series array (with P. Colet and Wiesenfeld), Physical Review Letters 76 (1996), 404–407. Collective dynamics of 'small-world' networks (with D. J. Watts), Nature 393 (1998), 440–442. Exploring complex networks, Nature 410 (2001), 268–276. Sync: The Emerging Science of Spontaneous Order, Hyperion, 2003. Crowd synchrony on the Millennium Bridge (with D. M. Abrams, B. Eckhardt, A. McRobie, and E. Ott), Nature 438 (2005), 43–44. Modeling walker synchronization on the Millennium Bridge (with D. M. Abrams, B. Eckhardt, A. McRobie, and E. Ott), Physical Review E 75 (2007), 021110. Synchronization in the Winfree model of coupled nonlinear oscillators (with D. Dane Quinn and Richard Rand), Physical Review E 75 (2007), 036218. The spectrum of the partially locked state for the Kuramoto model (with Renato Mirollo), Journal of Nonlinear Science 17 (2007), 309–347. The end of insight; in What is Your Dangerous Idea? Today's leading thinkers on the unthinkable (John Brockman, ed.), Harper Perennial, New York, 2007, pp. 130–131. Understanding sleep; in What Are You Optimistic About? Today's leading thinkers on why things are good and getting better (John Brockman, ed.), Harper Perennial, New York, 2007, pp. 337–339. A journey to baseball’s alternate universe (with Samuel Arbesman), The New York Times, Sunday Op-Ed page (30 March 2008). Last modified: July 20, 2009 |
