SCIENTIFIC PROGRAMS AND ACTIVITIES

THE FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES 20th ANNIVERSARY YEAR July 2012 FOCUS PROGRAM ON GEOMETRY, MECHANICS AND DYNAMICS the Legacy of Jerry Marsden at The Fields Institute, Toronto Organizing Committee: Dong Eui Chang, Professor, University of Waterloo. Darryl Holm, Professor of Applied Mathematics, Imperial College London. George W. Patrick, Professor, University of Saskatchewan (principal organizer). Tudor Ratiu, Director of the Bernoulli Center, EPFL

Jerry Marsden, a pre-eminent applied mathematician, passed away September 21, 2010. He was the Carl F. Braun Professor of Engineering, Control and Dynamical Systems and Applied and Computational Mathematics, at the California Institute of Technology. His honors include: Fellow of the Royal Society, Fellow of the Royal Society of Canada, von Neumann Lecture and Prize (SIAM), Max Planck Research Award for Mathematics and Informatics, the Norbert Wiener Prize (AMS), and the Thomas K. Caughey Dynamics Award (ASME). In addition, he was the first director of the Fields Institute.

"Remembering Jerry Marsden", an obituary
Obituary: Jerry Marsden

Overview of the Program

The program will focus the topics on areas in which Jerry had significant contributions, or extend his lines of research, or, more generally, focus on a subject that we know would have been of interest to Jerry. The following themes will be targeted:

• Symplectic, Poisson, and Dirac geometry, reduction.
• Bifurcation theory.
• Geometric fluid dynamics and elasticity.
• Averaged hydrodynamics and Lagrangian coherent states.
• Space mission design.
• Geometric and structure preserving integration.
• Control and nonholonomic mechanics.
• Field theory and relativity.

The Focus Program will be generally be scheduled as follows. Participants who would like to speak or give a Minisymposium during the Program may contact the principal organizer George Patrick patrick(at)math.usask.ca

Week of July 3 - 6, 2012
Geometric and Structure Preserving Integration

	Tuesday (July 3)	Wednesday (July 4)	Thursday (July 5)	Friday (July 6)
2:00-3:00	Organization Meeting with Participants	Mathieu de Brun Room 210	Darryl D. Holm Fermat's Principle and the Geometric Mechanics of Ray Optics (slides) Room 210	Darryl D. Holm Fermat's Principle and the Geometric Mechanics of Ray Optics (slides) Room 210
3:00-3:30	Darryl Holm Fermat's Principle and the Geometric Mechanics of Ray Optics	Coffee Break	Coffee Break	Coffee Break
3:30-4:00		Darryl D. Holm Fermat's Principle and the Geometric Mechanics of Ray Optics (slides) Room 210	Cristina Stoica N-body Problem Bahen Centre: Room 1190	Holger Dullin Lie-Poisson structure of the reduced N-body problem Room 210
4:00-4:30	Christian Lessig Geometry of Light Transport Bahen Center, Room 1190
4:30-5:00		Henry Jacobs Room 210	Melvin Leok General Techniques for Constructing Variational Integrators Bahen Centre: Room 1190	Tomasz Tyranowski Adaptive Variational Integrator Room 210
5:00-5:30

Week of July 09-13, 2012
Geometry and mechanics
Location: Fields Institute, Room 210

	Monday (July 9)	Tuesday (July 10)	Wednesday (July 11)	Thursday (July 12)	Friday (July 13)
11:00-12:00	Cesare Tronci University of Surrey Collisionless kinetic theory of rolling molecules	Jaume Llibre Universitat Autonoma de Barcelona On the central congurations of the Nbody problem	Debra Lewis University of California Santa Cruz Colloquium	Martins Bruveris Imperial College London Geometry of Image Registration: Diffeomorphism group and Momentum maps (Starts at 10:45am)	Vakhtang Putkaradze University of Alberta Colloquium
12:00-2:00	Lunch	Lunch	Lunch	Lunch	Lunch
2:00-3:00	Alex Castro Pontifícia Universidade Católica do Rio de Janeiro Summer School	Alex Castro Pontifícia Universidade Católica do Rio de Janeiro Summer School	Henry Jacobs California Institute of Technology Summer School	George Patrick University of Saskachewan Variational integrators	Martins Bruveris Imperial College London Geometry of Image Registration: Diffeomorphism group and Momentum maps
3:00-3:30	Tea Break	Tea Break	Tea Break	Tea Break
3:30-4:30	Ale Cabrera Universidade Federal Rio de Janeiro Geometric phases in partially controlled mechanical systems	François Gay-Balmaz Ecole Normale Superieure de Paris Dual pairs in fluid dynamics	David Meier Imperial College London Quantum Splines (Ends at 4pm)	Ale Cabrera Universidade Federal Rio de Janeiro Geometric phases in partially controlled mechanical systems	Tea Break
					Olivier Verdier NTNU Geometric Generalisations of the Shake and Rattle methods (Starts at 4pm)
4:30-5:30	Marcel Oliver Jacobs University Backward error analysis for symplectic Runge–Kutta Methods on Hilbert spaces	Dong Eui Chang University of Waterloo Damping-Induced Self Recovery Phenomenon in Mechanical Systems with an Unactuated Cyclic Variable	Darryl D. Holm Imperial College London Fields Institute Colloquium in Applied Mathematics Momentum Maps, Image Analysis & Solitons (Begins at 4:10pm, Room 230)	Felipe Arrate Basque Center for Applied Mathematics Cardiac Electrophysiology Model on the moving heart

Week of July 16-20, 2012
Control and nonholonomic mechanics; Fluid dynamics and elasticity; Field theory and relativity

In the third week of the program, participants of the symposia during the first two weeks will meet in informal collaborations, and there will be a summer school on Mechanics and Geometry in Canada (MAGIC).

	Monday (July 16)	Tuesday (July 17)	Wednesday (July 18)	Thursday (July 19)	Friday (July 20)
9:30-10:30	Jedrzej Sniatycki University of Calgary Differential Geometry of Singular Spaces and Reduction of Symmetries	Jedrzej Sniatycki University of Calgary Differential Geometry of Singular Spaces and Reduction of Symmetries	Jedrzej Sniatycki University of Calgary Differential Geometry of Singular Spaces and Reduction of Symmetries	Jedrzej Sniatycki University of Calgary Differential Geometry of Singular Spaces and Reduction of Symmetries	Tanya Schmah University of Toronto Reduction of systems with configuration space isotropy
10:30-11:00	Coffee Break	Coffee Break	Coffee Break	Coffee Break	Coffee Break
11:00-12:00	Tudor Ratiu Ecole Polytechnique Fédérale de Lausanne The reduced variation principle for free-boundary continua	Klas Modin Chalmers University of Technology Higher dimensional generalisation of the $\mu$--Hunter--Saxton equation	David Martin de Diego Review talk about nonholonomic dynamics	J.C. Morrero University of La Laguna Hamilton-Jacobi equation and integrability	Anthony Bloch University of Michigan Continuous and Discrete Embedded Optimal Control Problems
12:00-2:00	Lunch	Lunch	Lunch	Lunch	Lunch
2:00-3:00	Henrique Bursztyn IMPA, Rio de Janeiro An Introduction to Dirac Structures	Paula Balseiro Universidade Federal Fluminense Twisted brackets in nonholonomic mechanics	Edith Padrón Hamilton-Jacobi equations and nonholonomic dynamics	Dimitri Zenkov North Carolina State University The Hamel equations and applications to nonholonomic systems	Miguel Rodriguez-Olmos Technical University of Catalonia Hamiltonian bifurcations from stable branches of relative equilibria
3:00-3:30	Tea Break	Tea Break	Tea Break	Tea Break	Tea Break
3:30-5:30	Leonardo Colombo Instituto de Ciencias Matemáticas Higher-order Lagrange-Poincaré reduction for optimal control of underactuated mechanical systems	Lyudmyla Grygor'yeva, Juan-Pablo Ortega and Stanislav Zub Working group on problems of non-contact confinement of rigid bodies (Ends at 5:00pm)     Reception (Begins at 5:00pm)	David Meier, Francois-Xavier Vialard, Martins Bruveris, Francois Gay-Balmaz and Chris Burnett Mini-symposium on image registration	Richard Montgomery University of California, Santa Cruz Classical Few-body Progress Jeffery Lawson Western Carolina University A heuristic approach to geometric phase Tomoki Ohsawa University of California, San Diego	Richard Montgomery University of California, Santa Cruz Classical Few-body Progress Shane Ross Virginia Tech Lagrangian coherent structures
	Gabriela Depetri Universidade Estadual de Campinas Geodesic chaos around black-holes with magnetic fields
	Miguel Vaquero Instituto de Ciencias Matemáticas Hamilton-Jacobi for Generalized Hamiltonian Systems				Eder Mateus Universidade Federal de Sergipe Spatial isosceles three body problem with rotating axis of symmetry Adriano Regis Universidade Federal Rural de Pernambuco Vortices on the triaxial ellipsoid: a movie show
					Brian Seguin McGill University A transport theorem for irregular evolving domains 5:30pm-6:00pm

Week of July 23-27, 2012
Conference on Geometry, symmetry, dynamics, and control: The legacy of Jerry Marsden.

	Monday (July 23)	Tuesday (July 24)	Wednesday (July 25)	Thursday (July 26)	Friday (July 27)
9:00-10:10	Wang Sang Koon California Institute of Technology Control of a Model of DNA Division Via Parametric Resonance	David Ebin Stony Brook University Reflections on the paper, "Groups of diffeomorphisms and the motion of an incompressible fluid"	Juan-Pablo Ortega Université de Franche-Comté/Centre National de la Recherche Scientifique Stochastic Hamiltonian Systems	Anthony Bloch University of Michigan The geometry of integrable and gradient flows and dissipation (Audio of talk)	Hiroaki Yoshimura Waseda University Dirac Structures, Variational Principles and Reduction in Mechanics --- Toward Understanding Interconnection Structures in Physical Systems (Audio of talk)
10:10-10:40	Coffee Break	Coffee Break		Coffee Break	Coffee Break
10:40- 11:50	Henry Jacobs Caltech; Imperial College London Is swimming a limit cycle?	Mark Gotay University of British Columbia Momentum Maps and Classical Fields	Joris Vankerschaver University of California, San Diego Fluid-Structure Interactions: Geometric and Numerical Aspects	Marco Castrillón López Universad Complutense de Madrid Higher order covariant Euler-Poincaré (Audio of talk)	Arthur Fischer UCSC The Legacy of Jerry Marsden's Early Career Work in Riemannian Geometry and General Relativity
11:50-2:00	Lunch	Lunch	Lunch	Lunch	Lunch
2:00-2:40	Banavara Shashikanth New Mexico State University Vortex dynamics of classical fluids in higher dimensions	Dong Eui Chang University of Waterloo Control of mechanical systems	2:00-3:00 Introduction by Mark Gotay, PIMS 2012 PIMS Marsden Memorial Lecturer - Richard Montgomery (Audio of talk)	Antonio Hernández-Garduño UAM-I, Mexico Algebra and reduction of the three vortex problem (Audio of talk)	Elisa Guzmán Universidad de La Laguna Reduction of Lagrangian submanifolds and Tulczyjew's triple (Audio of talk)
2:40-3:20	George Patrick University of Saskatchewan Geometry and the analysis of geometric numerical algorithms	Jair Koiller Getulio Vargas Foundation A gentle introduction to Microswimming: geometry, physics, analysis		Scott Kelly University of North Carolina at Charlotte (Audio of talk)	Ari Stern University of California, San Diego Symplectic groupoids and discrete constrained Lagrangian mechanics
3:20-3:50	Tea Break	Tea Break	Tea Break (3:00-3:30)	Tea Break	End
3:50-4:30	Tom Mestdag Ghent University Anholonomic frames in nonholonomic mechanics	Melvin Leok University of California, San Diego Discrete Hamiltonian Variational Integrators and Discrete Hamilton--Jacobi Theory	3:30-5:30 Reflections on Jerry Marsden: Life & Work Talks and Panel Session (Audio of talks)	William F. Shadwick Omega Analysis Limited From the Geometry of Extreme Value Distributions to 'Laws of Mechanics' in Financial Markets
4:30-5:10	Daniel Offin Queen's University	Stephen Preston University of Colorado Geodesic equations on contactomorphism groups		Andrea Dziubek, Edmond Rusjan SUNY IT A Model for the Retina Including Blood Flow and Deformation (Audio of talk)

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