78 DS09 Abstracts IP0 IP3 Jrgen Moser Lecture: Catastrophes, Symmetry- Network Topology: Sensors and Systems Breaking, Synchrony-Breaking Networks arise in innumerable contexts from mobile com- The ideas that surrounded catastrophe theory (codimen- munications devices, to environmental sensors nets, to bi- sion, unfoldings, organizing centers, ...) have shaped much ological systems at all scales. This talk explores the re- progress in bifurcation theory during the past forty years lationships between what happens on the network nodes and, indeed, in many of its applications. I will try to trace (signals, sensing, dynamics) and the underlying spatial dis- some of these developments and to indicate why this same tribution of the nodes — an especially delicate interplay in way of thinking might lead to interesting discoveries in net- the context of coordinate-free, non-localized systems. The work dynamics. key tools are an adaptation of homology theory. Algebraic topology yields an enrichment of network topology that in- Martin Golubitsky tegrates cleanly with statistics and dynamics of networks, Ohio State University and which allows for solutions to problems of coverage, Mathematical Biosciences Institute communication, and control.
[email protected] Robert W. Ghrist University of Pennsylvania IP1
[email protected] Collapse of the Atlantic Ocean Circulation The Atlantic Ocean Circulation is sensitive to the patterns IP4 of atmospheric forcing. Relatively small changes in atmo- Mechanisms of Instability in Nearly Integrable spheric conditions may lead to a spectacular collapse of Hamiltonian Systems Atlantic Ocean currents, with a large impact on European climate. In ocean-climate models, a collapse is associated There are many systems that appear in applications that with the existence of saddle-node bifurcations.