# SCIENTIFIC PROGRAMS AND ACTIVITIES

July 28, 2015

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
 Confirmed Participants Schedule of Activities Audio and Slides of July 23-27, Conference Speaker Abstracts Reimbursement information for funded participants

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.

### 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, 2012Conference 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 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 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 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