Organizing Committee
Abstract

This workshop focuses on topics at the interface of classical mechanics, differential geometry, and computer experiments. The directions of current research to be explored at the workshop include the study of invariants and complete integrability of geometrically motivated differential equations (in particular, vehicle motion, tire track geometry, and smoke ring equations), sub-Riemannian geometry, geometric control, nonholonomic systems (such as e.g. bicycle stability and nonholonomic methods in billiard problems), computational methods in mechanics and dynamics (including geometric integrators, biological applications, etc.).

The goal of the workshop is to explore broad applications of the mechanical approach to geometry and geometric one to classical mechanics, to foster interaction between researchers in the above areas, with a view of finding new domains for applications of these fertile ideas.

Special Issue on Integrability in Mechanics and Geometry: Theory and Computations in honour of Mark Levi

Confirmed Speakers & Participants

Workshop Schedule

Monday, June 1, 2015
TimeEventLocationMaterials
8:30 - 8:55Registration - Integrability in Mechanics and Geometry: Theory and Computations 11th Floor Collaborative Space 
8:55 - 9:00Welcome - ICERM Director11th Floor Lecture Hall 
9:00 - 9:45Realizing Collinear Sequences with the Three-Body Problem - Richard Montgomery, University of California, Santa Cruz11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15Iterating evolutes and involutes- theory and experiments - Sergei Tabachnikov, ICERM11th Floor Lecture Hall
11:30 - 12:15Surprises of nonholonomy - Tadashi Tokieda, University of Cambridge 11th Floor Lecture Hall 
12:30 - 2:30Break for Lunch  
2:30 - 3:15Stability of some dissipative systems and efficient estimates on the existence of quasi-periodic attractors - Alessandra Celletti, University of Rome11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45Traveling waves in lattices - Mark Levi, Pennsylvania State University11th Floor Lecture Hall
5:00 - 6:30Welcome Reception11th Floor Collaborative Space 
Tuesday, June 2, 2015
TimeEventLocationMaterials
9:00 - 9:45Taylor Constraint in Cartesian Coordinates - Maxim Arnold, University of Texas at Dallas11th Floor Lecture Hall 
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative 
10:30 - 11:15Spaces of directed paths. - Yuliy Baryshnikov, University of Illinois 11th Floor Lecture Hall
11:30 - 12:15The evolution of spatial critical points under abrasion - Gabor Domokos, Budapest University11th Floor Lecture Hall
12:30 - 2:30Break for Lunch  
2:30 - 3:15Stability for the multidimensional rigid body and algebraic curves - Anton Izosimov, University of Toronto11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collabortive Space 
4:00 - 4:45Geometric (Statistical and Continuum) Mechanics of Ribbons - L. Mahadevan, Harvard University11th Floor Lecture Hall 
Wednesday, June 3, 2015
TimeEventLocationMaterials
9:00 - 9:45Von Karman vortex streets and solitons - Alexander Veselov, Loughborough University11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15Hirota-Kimura discretizations of integrable systems with quadratic vector fields- theory and mathematical experiments - Yuri Suris, Technical University of Berlin11th Floor Lecture Hall
11:30 - 12:15Non-integrability of natural Hamiltonian systems- tricks and methods - Vladimir Matveev, Friedrich-Schiller-Universität, Jena11th Floor Lecture Hall
12:30 - 12:40Group Photo11th Floor Lecture Hall 
12:40 - 2:15Break for Lunch  
2:15 - 3:00Ray optics for thin films - Ron Perline, Drexel University11th Floor Lecture Hall
3:00 - 5:00Poster Session and Coffee/Tea Break11th Floor Lecture Hall and Collaborative Space 
Thursday, June 4, 2015
TimeEventLocationMaterials
9:00 - 9:45Rational degenerations of $m$-curves and totally positive Grassmannians - Simonetta Abenda, University of Bologna11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15Rolling of projective planes with G2-symmetry - Gil Bor, Center of Investigations in Mathematics11th Floor Lecture Hall
11:40 - 12:25The flat trefoil and other oddities - Joel Langer, Case Western Reserve University11th Floor Lecture Hall
12:40 - 2:30Break for Lunch  
2:30 - 3:15Intersection of quadrics and 2-dimensional Abelian varieties, an experimental study - Yuri Fedorov, Polytechnic University of Catalonia11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45Integrable Geometric Flows in Diverse Geometries - Thomas Ivey, College of Charleston11th Floor Lecture Hall
Friday, June 5, 2015
TimeEventLocationMaterials
9:00 - 9:45Space-Time Finite-Element Exterior Calculus and Variational Discretizations of Gauge Field Theories - Melvin Leok, University of California, San Diego11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15Discrete nonholonomic mechanics on Lie groups - Luis García-Naranjo, National Autonomous University of Mexico11th Floor Lecture Hall
11:30 - 12:15 Skew Mean Curvature Flow - Chong Song, Xiamen University11th Floor Lecture Hall
12:30 - 2:30Break for Lunch  
2:30 - 3:15 Hamel's Formalism and Constrained Mechanics - Dmitry Zenkov, North Carolina State University11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45The Poincare-Hopf Theorem in Nonholonomic Mechanics - Oscar Fernandez, Wellesley College11th Floor Lecture Hall

Lecture Videos

Discrete nonholonomic mechanics on Lie groups

Luis García-Naranjo
National Autonomous University of Mexico
June 5, 2015