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.

Image for "Integrability in Mechanics and Geometry: Theory and Computations"

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

Confirmed Speakers & Participants

Talks will be presented virtually or in-person as indicated in the schedule below.

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee

Workshop Schedule

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

Lecture Videos

The Poincare-Hopf Theorem in Nonholonomic Mechanics

Oscar Fernandes
Wellesley College
June 5, 2015
Integrability in Mechanics and Geometry: Theory and Computations
Play     Abstract

Hamel's Formalism and Constrained Mechanics

Dmitry Zenkov
NC State University
June 5, 2015
Integrability in Mechanics and Geometry: Theory and Computations
Play     Abstract

Skew Mean Curvature Flow

Chong Song
Xiamen University
June 5, 2015
Integrability in Mechanics and Geometry: Theory and Computations
Play     Abstract

Discrete nonholonomic mechanics on Lie groups

Luis Garcia-Naranjo
UNAM
June 5, 2015
Integrability in Mechanics and Geometry: Theory and Computations
Play     Abstract     Slides

Space-Time Finite-Element Exterior Calculus and Variational Discretizations of Gauge Field Theories

Melvin Leok
UCSD
June 5, 2015
Integrability in Mechanics and Geometry: Theory and Computations
Play     Abstract     Slides

Integrable Geometric Flows in Diverse Geometries

Thomas Ivey
College of Charleston
June 4, 2015
Integrability in Mechanics and Geometry: Theory and Computations
Play     Abstract

Rolling of projective planes with G2-symmetry

Gil Bor
CIMAT
June 4, 2015
Integrability in Mechanics and Geometry: Theory and Computations
Play     Abstract     Slides

Rational degenerations of $m$-curves and totally positive Grassmannians

Simonetta Abenda
Università di Bologna
June 4, 2015
Integrability in Mechanics and Geometry: Theory and Computations
Play     Abstract

Non-integrability of natural Hamiltonian systems- tricks and methods

Vladimir Matveev
University of Jena
June 3, 2015
Integrability in Mechanics and Geometry: Theory and Computations
Play     Abstract

Hirota-Kimura discretizations of integrable systems with quadratic vector fields- theory and mathematical experiments

Yuri Suris
Technische Universität Berlin
June 3, 2015
Integrability in Mechanics and Geometry: Theory and Computations
Play     Abstract

Stability for the multidimensional rigid body and algebraic curves

Anton Izosimov
University of Toronto
June 2, 2015
Integrability in Mechanics and Geometry: Theory and Computations
Play     Abstract

The evolution of spatial critical points under abrasion

Gabor Domokos
Budapest University of Technology and Economics
June 2, 2015
Integrability in Mechanics and Geometry: Theory and Computations
Play     Abstract

Stability of some dissipative systems and efficient estimates on the existence of quasi-periodic attractors

Alessandra Celletti
University of Roma
June 1, 2015
Integrability in Mechanics and Geometry: Theory and Computations
Play     Abstract

Iterating evolutes and involutes- theory and experiments

Sergei Tabachnikov
ICERM and Penn State
June 1, 2015
Integrability in Mechanics and Geometry: Theory and Computations
Play     Abstract     Slides

Realizing Collinear Sequences with the Three-Body Problem

Richard Montgomery
University of California - Santa Cruz
June 1, 2015
Integrability in Mechanics and Geometry: Theory and Computations
Play     Abstract