Activity

Universitat Politècnica de Catalunya - BarcelonaTech, Barcelona, Spain. December 11-13, 2013.

Introduction:

The 8th International Young Researchers Workshop on Geometry, Mechanics and Control will be the eighth in a series of workshops that have previously taken place in Madrid (20062007, 2012), Barcelona (2008), Ghent (2009), La Laguna (2010) and Coimbra (2012). Its goal is to bring together young researchers working in geometric mechanics and control theory and to offer a platform to present the results of their research to an international audience.

The core of the workshop consists on 3 mini-courses, of 4 hours each, which serve as an introduction to different topics related to geometric structures in mechanics and control theory. The courses will be at a PhD and postdoctoral level, and it is expected that the young researchers will be, at the end of the workshop, able to access to the recent literature on the corresponding topics.

Along with the courses, there will be contributed short talks (30 minutes) and a poster session. Attendance is, of course, open to anyone, but in particular young researchers (PhD-students, recent PhD's) are encouraged to submit or poster proposal.

The following is a non-exhaustive list of topics that can be covered during the workshop:

  • Geometry: (multi)symplectic geometry, Poisson and Jacobi manifolds, Lie groups, Lie algebroids and Lie groupoids.
  • Mechanics: Lagrangian and Hamiltonian systems, non-holonomic mechanics, calculus of variations, mechanical systems with symmetry, conservation laws and reduction, classical field theories, geometric integration of mechanical systems, geometric quantization.
  • Control: optimal control theory, control of mechanical systems, geometric control.

Latest news:

Notes of the course Symplectic geometry of the moduli space of flat connections uploaded.

Important dates:

Registration: Closed.

Financial support: Closed.

Poster / Short talks: Closed.

Courses:

  • Camilo Arias Abad (Universität Zürich, Switzerland): Symplectic geometry of the moduli space of flat connections (Course notes)

    Abstract: The moduli space of flat connections on a principal G-bundle over a compact surface admits a symplectic structure which was originally described by Atiyah-Bott [1], via symplectic reduction of an infinite dimensional space. The purpose of this minicourse is to study some topological properties of these symplectic spaces.

    The moduli spaces of flat connections admit a finite dimensional description: as representation varieties of the fundamental group of the surface. The comparison between the finite and infinite dimensional descriptions will be central to the course.

    Another important aspect that will be discussed is the use of equivariant Morse theory in the study of the topology of moduli
    spaces.

    Some fundamental references for the material to be covered include:

    [1] Atiyah, M.F. and Bott, R., The Yang-Mills equations over Riemann surfaces, Phil. Trans. R. Soc. Lond. A 308 (1982), 523-615.

    [2] R. W. Goldman, The symplectic nature of fundamental groups of surfaces, Adv. Math., 54 (1984), pp. 200–225

    [3] R. Bott, Morse theory indomitable, Publ. Math. IHES 68, 99-114 (1988).

    [4] A. Weinstein, The symplectic structure on moduli space, Floer memorial volume, Birkhauser (1995).

  • Philipp Bader (Universidad Politécnica de Valencia, Spain): Geometric integrators with applications to optimal control problems (Course notes)

    Abstract: During the last decades, the community of numerical analysts has shifted from all-purpose methods to schemes that are designed to solve a particular problem efficiently by putting as much information about the system as possible into the numerical integrator. Geometric numerical integrators obtained their name after it was noticed that they preserved certain geometric properties of the exact solution of a differential equation and could be considered prototypes of this paradigm.

    In this series of lectures, an introduction to geometric numerical integrators will be given, the benefits of such methods will be discussed and applications to problems in optimal control will be presented.
    On the integrator side, we will emphasize on splitting methods and the Magnus expansion. The treated examples for controlled systems will come from classical and quantum mechanics and a rudimentary understanding of Hamiltonian systems will be helpful.

    It is useful to have a rough idea about the numerical integration of ordinary differential equations and a basic knowledge of Lie algebras and Lie groups.

    The main reference is
    E. Hairer, C. Lubich and G. Wanner, Geometric Numerical Integration, Springer, Berlin, 2006

  • François-Xavier Vialard (Université Paris-Dauphine, France): Applications of geometric mechanics to computational anatomy

    Abstract: We will provide an overview of state of the art applications of geometric mechanics in computational anatomy. Startingfrom the problem of diffeomorphic registration of images, we will present the standard model of large deformations by diffeomorphisms (i.e. geodesics on group of diffeomorphisms for right-invariant metrics) from a geometric viewpoint but with a particular focus on its analytical setting and the numerical algorithms currently used in practice. Among other developments, we will present the problem of template estimation and higher-order models for spatiotemporal image registration. We will then conclude with open problems and new directions. This minicourse will use standard geometric mechanics concepts and optimal control tools. The bibliography includes among others:

    [1] Younes, L.: Shapes and Diffeomorphisms, Springer

    [2] Beg, M.F., Miller, M.I., Trouve, A., Younes, L.: Computing large deformation metric mappings via geodesic flows of diffeomorphisms. Int. J. Comput. Vision

    [3] Bruveris M., Risser L., Vialard F.X., Mixture of Kernels and Iterated semidirect Product of Diffeomorphisms Groups. SIAM MMS,

    [4] F. Gay-Balmaz, D. D. Holm, D. M. Meier, T. S. Ratiu and F.X. Vialard, Invariant higher-order variational problems, CMP

    [5] Overview of the Geometries of Shape Spaces and Diffeomorphism Groups, Martin Bauer, Martins Bruveris, Peter W. Michor.

Schedule:

This is a tentative shedule to make easier the travel arrangements. It will be updated as the workshop gets closer.

  Wednesday 11 Thursday 12 Friday 13
9:00-9:30 Registration    
9:30-11:00 Philipp Bader François-Xavier Vialard Camilo Arias Abad
11:00-11:30 COFFEE
11:30-13:00 François-Xavier Vialard Camilo Arias Abad Philipp Bader
13:00-15:00 LUNCH
15:00-16:00 Camilo Arias Abad Philipp Bader François-Xavier Vialard
16:00-16:30 García-Naranjo Navarro Fortney
16:30-17:00 COFFEE Vaquero COFFEE
17:00-17:30 Sardón POSTER-COFFEE Castro
17:30-18:00 Apraiz Howard
18:00-18:30 Chhabra   Novak
21:00   CONFERENCE DINNER  

 

Short talks

  • Apraiz: Null-Control and Measurable Sets
  • Castro: Some connections between parallel parking and real algebraic geometry
  • Chhabra: A three-step dynamical reduction of nonholonomic multi-body systems
  • Fortney: A Geometric Relationship Between Implicitly Defined Hamiltonian Systems and Pseudo-Gradiant Systems
  • García-Naranjo: Relative equilibria for the n-body problem in spaces of constant negative curvature
  • Howard: The Monster Tower and Connections to Sub-Riemannian Geometry
  • Navarro: The inverse problem of the calculus of variations on the bundle of metrics
  • Novak: Integrable system on the cotangent bundle of two-sheeted hyperboloid
  • Sardón: Lie-Hamilton systems on the plane: properties, classification and applications
  • Vaquero: Hamilton-Jacobi for generalized hamiltonian systems

Registration:

Registration is closed.

Financial Support:

There are some funds available to support young participants.

Lodging reservation:

We suggest the following university residences. In order to book your stay, please contact any of them directly mentioning your participation in the "8 Young Researchers Workshop UPC". Should you prefer an alternative accomodation, the variety of hotels in Barcelona is pretty wide.

Residència d'Investigadors

This residence hall is located in the city centre, and is well communicated with the conference venue by the metro line L3 (green line). All rooms include their own bathroom, television and wifi.

Webpage / investigadorsatresa [dot] es

Residència Torre Girona

This residence hall is located near the conference venue, at the North Campus of the University. All rooms include their own bathroom, television and wifi.

Webpage / torregironaatresa [dot] es

Residència Campus del Mar

This residence hall is close to the city center, by the beach, but it has a longer commute time with the conference venue. All rooms include their own bathroom, television and wifi.

Webpage / campusdelmaratresa [dot] es

Participants:

Updated on December 13, 2013

Jone Apraiz Universidad del País Vasco Spain
María Barbero Universidad Carlos III de Madrid - ICMAT Spain
Lucía Búa Devesa Universidade de Santiago de Compostela (USC) Spain
Alex Castro PUC-Rio Brazil
Robin Chhabra University of Toronto Canada
Leonardo Colombo Instituto de Ciencias Matemáticas (ICMAT) Spain
Marta Farré ICMAT Spain
Jon Pierre Fortney Zayed University U.A.E.
Luis García-Naranjo UNAM Mexico
Irina Mihaela Gheorghiu University of Zaragoza Spain
Xavier Gàcia Technical University of Catalonia (UPC) Spain
Wyatt Howard IMPA U.S.A.
Jair Koiller EMAP/FGV Brazil
Jorge Alberto Jover Galtier Universidad de Zaragoza Spain
Adela Latorre Universidad de Zaragoza Spain
Du Li University of Goettingen Germany
Miguel Muñoz Technical University of Catalonia (UPC) Spain
Jose Navarro Universidad de Extremadura Spain
Tina Novak University in Ljubljana, Faculty of Mechanical engineering Slovenia
Boris Osorno Torres Utrecht University The Netherlands
Alexander Petkov Faculty of Mathematics and Informatics, University of Sofia "St. Kliment Ohridsky" Bulgaria
Pere Daniel Prieto Martínez Technical University of Catalonia (UPC) Spain
Xavier Ramos Olivé Technical University of Catalonia (UPC) Spain
Miguel Rodríguez-Olmos Technical University of Catalonia (UPC) Spain
Narciso Román Roy Technical University of Catalonia (UPC) Spain
Cristina Sardon Universidad de Salamanca Spain
Miquel Teixidó Technical University of Catalonia (UPC) Spain
Miguel Vaquero ICMAT Spain
Rupert Venzke Universidade de Sao Paulo Brazil

Committees:

Organizing Committee

  • Xavier Gràcia (Universitat Politècnica de Catalunya, Spain)
  • Pere Daniel Prieto-Martínez (Universitat Politècnica de Catalunya, Spain)
  • Miguel Rodríguez-Olmos (Universitat Politècnica de Catalunya, Spain)
  • Narciso Román-Roy (Universitat Politècnica de Catalunya, Spain)
  • Miguel Teixidó Román (Universitat Politècnica de Catalunya, Spain)

Scientific Committee

  • Paula Balseiro (Universidad Federal Fluminense, Brazil)
  • María Barbero (Universidad Carlos III de Madrid and ICMAT, Spain)
  • Cédric M. Campos (Instituto de Ciencias Matemáticas, Madrid, Spain)
  • Sebastián Ferraro (Universidad Nacional del Sur, Argentina)
  • François Gay-Balmaz (CNRS, École Normale Supérieure, France)
  • Marin Kobilarov (Caltech, USA)
  • Miguel Rodríguez-Olmos (Universitat Politècnica de Catalunya, Spain)
  • Marco Zambon (Universidad Autónoma de Madrid and ICMAT, Spain)

How to get here:

The conference will take place at the Sala d'Actes of the Facultat de Matemàtiques i Estadística (FME). The easiest way to arrive to the FME is taking the metro, line L3 (the green line), direction Zona Universitària. Get off at Palau Reial or Zona Universitària. The FME is 5 minutes by walk from both stops. Have a look at the map on the right.

You can also get to the FME by bus (lines L7, L33, L54, L60, L68, L74, L75, L133) or tram (lines 1, 2 and 3). In both cases, get off at Palau Reial or Zona Universitària.

Click here to go to Google Maps' website.