Workshop

The aim of this workshop is to promote the interaction of researchers working on pure and applied aspects dynamical systems. It will feature a group of speakers from mathematics who are responsible for some of the ma advances in the theory of dynamical systems over recent years. They will be complemented with speakers working ispecific applied areas where dynamical systems ideas are used, such as neuroscience, atmospheric sciences, fluidschemical reactions. We plan to have overview talks the aim of which is for each of these groups to introduce thework and techniques to the other, and more specialized talks that center on specific recent advances. Schedule MONDAY, January 22 Welcome 9:15 AM -10:00 AM Smale, Steve: “Dynamics of emergence and flocking” 10:30 AM -11:15 AM Golubitsky, Martin: “Bifurcations in Coupled Systems” 11:15 AM -12:00 PM Kaloshin, Vadim: “Oscillatory motions, Arnold diffusion, and nonlocal instabilities for the planar 3 body problem” 12:00 PM – 1:30 PM LUNCH 1:30 PM - 2:30 PM Mather, John: “Aspects of Arnold Diffusion” 3:00 PM - 3:45 PM Levi, Mark: “Simple examples of Arnold diffusion” TUESDAY, January 23 9:00 AM - 9:45 AM Pesin, Yakov: “Genericity of chaotic dynamics” 9:45 AM -10:30 AM Bunimovich, Leonid: “Dynamical Networks” 11:00 AM -12:00 PM Young, Lai-Sang: “Rank one attractors and weak chaos” 12:00 PM – 2:00 PM LUNCH 2:00 PM - 3:00 PM Chernov, Nikolai: “Chaotic billiards” 3:30 PM - 4:15 PM Dolgopyat, Dmitry: "Recurrence properties of finite horizon Galton board" 4:15 PM - 5:00 PM Pikovsky, Arkady: “Autonomous coupled oscillators with hyperbolic strange attractors” 5:00 PM – 6:00 PM Welcome Reception WEDNESDAY, January 24 9:00 AM - 9:45 AM Evans, Craig : “PDE methods for weak KAM theory” 9:45 AM -10:30 AM Mischaikow, Konstantin: “Computational Dynamics and Homology” 11:00 AM -12:00 PM Doelman, Arjen: “Dynamics of reaction-diffusion patterns” 12:00 PM – 2:00 PM LUNCH 2:00 PM - 3:00 PM Sandstede, Bjorn: “Dynamics of nonlinear waves” 3:30 PM - 4:15 PM Titi, Edriss: “Dynamical Systems Approach to Turbulence” 4:30 PM - 6:30 PM Short Presentations THURSDAY, January 25 9:00 AM - 9:45 AM Zaslavsky, George: “Pseudochaos” 9:45 AM -10:30 AM Hunt, Brian: “Efficient Data Assimilation for Spatially Extended Systems” 11:00 AM -12:00 PM Jones, Christopher: “Do Invariant Manifolds Hold water?” 12:00 PM – 1:45 PM LUNCH 1:45 PM - 2:30 PM Marsden, Jerrold: “Lagrangian coherent structures” 2:30 PM - 3:15 PM Terman, David: “Reducing Neuronal Systems to Discrete Dynamics” UC Colloquium FRIDAY, January 26 9:00 AM - 9:45 AM Guckenheimer, John: “Bifurcations of Relaxation Oscillations” 9:45 AM -10:30 AM Lin, Kevin: “Reliable and Unreliable Behavior in Coupled Oscillator Networks” 11:00 AM -12:00 PM Kopell, Nancy: “Rhythmic dynamics of the nervous system” 12:00 PM – 1:30 PM LUNCH 1:30 PM - 2:15 PM Borisyuk, Alla: “The dynamic range of bursting in a network of respiratory pacemaker cells” 2:15 PM - 3:00 PM Holmes, Philip: “A central pattern generator for insect locomotion: Phase response curves, averaging and reduction ionic current models of bursting neurons” Short presentations by postdocs Wednesday, January 24, 4:30-6:30 Jorge deFreitas, University of Porto: Statistical stability for Hénon maps of the Benedicks-Carleson type Joyce Macabea, UC-Berkeley and MSRI: Quantifying and analyzing the pheromone response system for mating in yeast Mason Porter, Caltech: Nonlinearity Management in Optics Maria Leite, Purdue University: Coupled Systems of ODE's and Their Coupling Structure Nikola Popovic, Boston University: Mixed-mode oscillations and the canard phenomenon: an example Amit Apte, UNC-CH and MSRI: A Bayesian approach to data assimilation Aaron Hoffman, Boston University: Lattice Differential Equations Zoi Rapti, University of Illinois, Urbana-Champaign: Counting eigenvalues via the Evans function Abdul Kane, University of Toronto: Spatio-temporal patterns of activity in large scale neuronal networks Alice Jukes, Imperial College: Homoclinic bifurcation with symmetry Claire Postlethwaite, Northwestern University: Feedback control of patterns Vahagn Manukian, North Carolina State University: Traveling Waves of Surfactant Equations Emily Burkhead, Santa Fe Institute: A dynamical systems approach to the study of cellular automata Margaret Beck, University of Surrey and MSRI: Stability of solutions to PDEs Hamzi Boumediene, UC Davis and MSRI: Elements of the Dynamical Theory of Control Dan Wiley, Howard University and MSRI: Nonlocally Coupled Phase Oscillators Mark Demers, Fairfield University and MSRI: Stability of Statistical Properties via Lasota-Yorke Inequalities Anna Ghazaryan, University of North Carolina: Traveling Waves in Porous Media Combustion: Uniqueness of Waves of Small Thermal Diffusivity