COUPLED 60 A Focused Research Group Workshop Thursday - Sunday, February 3-6, 2005
Written by Krešimir Josić, University of Houston

The problem of analyzing the behavior of structured networks of interacting dynamical systems has received much attention recently. It is of fundamental interest in fields ranging from neuroscience and genetics to electrical and chemical engineering, and has led to the development of numerous mathematical techniques. The goal of the Coupled 60 Workshop was to bring together mathematicians and theoretical scientists from a variety of fields to exchange ideas on the subject. It also served as an introduction and overview of the applications and theory of coupled dynamical systems for the graduate students and postdoctoral fellows that constituted approximately half the audience. Moreover, it was an opportunity to mark the 60th birthdays of five participants: Mike Field, Marty Golubitsky, John Guckenheimer, Phil Holmes, and Ian Stewart.

The birthday boys: Mike Field, Ian Stewart, Marty Golubitsky, Phil Holmes and John Guckenheimer.

The workshop took place over four days on the campus of the University of Houston. The talks reflected the variety of problems and applications of the theory of networks of interacting dynamical systems. The following is a brief overview. Applications of the theory of coupled oscillators in neuroscience were discussed by Pete Ashwin, Paul Bressloff, Jack Cowan, Bard Ermentrout, Phil Holmes, Nancy Kopell, and Jon Rubin. The Houston Dynamical Systems Group (Toby Elmhirst, Mike Field, Marty Golubitsky, Krešo Josić, Matt Nicol, Ian Stewart, Andrew Török) presented their work on the theory and applications of coupled cell systems, with several talks focusing on open problems. Different perspectives on the dynamics of gene networks were given by Gabor Balaszi and Konstantin Mischaikow. Other participants presented their work on a number of other topics: celestial mechanics (Jerry Marsden), the analysis of synchrony in networks (Lou Pecora and Igor Belykh), the driven Van der Pol oscillator (John Guckenheimer), coupled cell models of solid flame waves (Bernie Matkowsky) and bifurcations and localization in coupled cell systems (Martin Krupa and Jeroen Lamb).

The first day of the workshop concluded with a well attended poster session. The 20+ posters covered a variety of topics, and it was difficult to visit all of them in one evening. Fortunately, they were displayed during most of the workshop, and so further discussions were possible. Many participants headed to the Houston Grand Opera for the performance of "Il Trovatore" after the second day of the workshop.

From left to right Andrew Oster, Eric Shea-Brown and Toby Elmhirst.		Banquet guests listening to Jerry Marsden.

A banquet held at the Houston Museum of Natural Science concluded the last full day of the workshop. Dinner followed aperitifs in the room housing the exceptional mineral collection (recently evaluated by no other than Steve Smale), and a tour of the butterfly center. This occasion was also used to mark the 60th birthdays of the five participants mentioned above. Although the combined output of this illustrious group would be sufficient to fill a decent library, their careers and achievements were finely summarized in a presentation by the Master of Ceremonies Jerry Marsden.

The workshop was sponsored by the National Science Foundation, the Department of Mathematics and the College of Natural Sciences and Mathematics at the University of Houston, and was organized by M. Golubitsky, K. Josić, M. Nicol, and A. Török.