Research Interests
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 nonlinear dynamics of language death; and the role of crowd synchronization in the wobbling of London’s Millennium Bridge on its opening day.
Grants
Cyber-Enabled Discovery and Innovation Program, “CDI Type II: Complex dynamics in the Internet: A computational analytic approach,” Co-Principal Investigator, National Science Foundation CCF-0835706, 2008-2012, $1,500,000.
“Nonlinear dynamics of oscillator networks,” Principal Investigator, National Science Foundation, 2004-2007, $524,061.
Integrative Graduate Education and Research Training (IGERT) grant, “Program in Nonlinear Systems,” Co-Principal Investigator, National Science Foundation DGE-0333366, 2003-2008, $3,436,000.
“Nonlinear dynamics of oscillator networks,” Principal Investigator, National Science Foundation, 2000-2003, $312,042.
Integrative Graduate Education and Research Training (IGERT) grant, “Program in Nonlinear Systems,” Principal Investigator, National Science Foundation, 1998-2003, $2,245,997.
“Mutual synchronization of biological oscillators,” Principal Investigator, National Science Foundation, 1996-1999, $180,000.
“Synchronization and communication in nonlinear optical systems,” Co-Principal Investigator, National Science Foundation, 1996-1999, $268,123.
“Nonlinear dynamics of oscillator arrays,” Principal Investigator, National Science Foundation, 1995-1998, $180,000.
“Large systems of coupled nonlinear oscillators in physics and biology,” Principal Investigator, National Science Foundation, 1992-1995, $75,000.
National Science Foundation Presidential Young Investigator Award, 1990–1995, $205,000
($125,000 base grant + $40,000 grant from AT&T + $40,000 matching money from NSF).
“Large systems of coupled nonlinear oscillators,” Principal Investigator, National Science Foundation, 1989–1991, $37,000.
National Science Foundation Postdoctoral Fellowship, 1986–89, $66,000.
Click here to view a PDF of my CV (coming)