13th International ICMAT Summer School on Geometry, Mechanics and Control

Sala Naranja, ICMAT, Madrid, Spain.

July 8-10, 2019.


Monday, 8 July, 2019
Wednesday, 10 July, 2019
Sala Naranja, ICMAT, Madrid, Spain.
Summer School on Geometry, Mechanics and Control

Organizing Committee

  • María Barbero Liñán (Universidad Politécnica de Madrid-ICMAT, Spain)
  • David Iglesias Ponte (Universidad de La Laguna, Spain)
  • David Martín de Diego (Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), Spain)
  • Edith Padrón (Universidad de La Laguna, Spain)

Scientific Committee

  • Anthony Bloch (University of Michigan, USA)
  • Jair Koiller (Fundação Getulio Vargas, Brazil)
  • Manuel de León (Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), Spain)
  • Juan Carlos Marrero (Universidad de La Laguna, Spain)
  • Eduardo Martínez (Universidad de Zaragoza, Spain)
  • Miguel Muñoz Lecanda (Universidad Politécnica de Cataluña, Spain)


9:00-10:30            E. MIRANDA/             J. MARGALEF M. MAZO M. MAZO
10:30-11:00 COFFEE
11:00-12:30           M. DE LEÓN/              J.C. MARRERO        M. DE LEÓN/         J.C. MARRERO         E. MIRANDA      
12:30-14:00 LUNCH
14:00-15:30 M. MAZO       J. MARGALEF/       E. MIRANDA         M. DE LEÓN/             J.C. MARRERO
16:00-16:30 COFFEE/POSTER
16:30:18:30 A. SIMOES





Roberta Ghezzi (Institut de Mathématiques de Bourgogne, France): Jacobi fields in sub-Riemannian geometry.

In Riemannian geometry, Jacobi fields along geodesics are defined as solutions of Jacobi equation, which involves the curvature tensor. Using a Lagrangian point of view, a classical result states that Jacobi fields are projections of solutions of the complete lift (to the double tangent) of the optimal control problem associated with the length-minimization problem on the base manifold. In a sub-Riemannian manifold M the metric tensor is only defined on a (nonholonomic) sub-bundle of TM and there is no analogous to the Levi-Civita connection. As a consequence, there is not a direct correspondent of Jacobi equation. Nevertheless, by a Hamiltonian approach which amounts to study the Legendre transformed optimal control problem on T^*M, Agrachev-Barilari-Rizzi provide in [Memoires AMS 2018] a notion of "Jacobi curve" on sub-Riemannian geodesics. Starting by the aforementioned interpretation of Jacobi fields in Riemannian geometry, we provide a new interpretation of Jacobi curves in sub-Riemannian geometry leading to the analysis of a Hamilton equation on T^*TM, from which a notion of sub-Riemannian curvature can be extracted. 

This is a joint work with D. Iglesias Ponte, J.C. Marrero, E. Padron 


Jacob Goodman (ICMAT, Spain): On the existence and uniqueness of Poincaré maps for systems with impulsive effects.

Ernesto Aranda Escolástico (University of Almería, Spain): Targeted formation control of Lagrangian systems with time delay.

Alexandre Simoes (ICMAT, Spain): Exact discrete Lagrangian for nonholonomic mechanics: an open problem.

Miguel Ángel Berbel (Instituto de Ciencias Matemáticas, Spain): Reduction (by stages) of Lagrange-Poincaré bundles.

Víctor M. Jiménez (ICMAT, Spain): Groupoids and distributions with applications to material bodies.

José Luis Carmona (Universidad Complutense de Madrid, Spain): Locally homogeneous Riemannian spaces.

Joaquim Brugués Mora (Universitat Politècnica de Catalunya, Spain): The construction of Floer homology.

Anastasia Matveeva (Universitat Politècnica de Catalunya, Spain): Quasi-Hamiltonian spaces and complex-valued moment maps.

Julia Lange (University of Warsaw, Poland): Foliated PDE Lie systems.

Iván Gutiérrez Sagredo (Universidad de Burgos, Spain): Quantum observers from Poisson-Lie geometry.

Daniel Wysocki (University of Warsaw, Poland): Gradations, Grassmann algebras and solutions to the classical Yang-Baxter equation.


Verónica Arroyo Rodríguez (Universidad Politécnica de Madrid-ICMAT, Spain): Control-oriented learning for formation control of mechanical systems.

Jordi Gaset (Universitat Politècnica de Catalunya, Spain): k-contact formalism: a framework for field theories with dissipation.

Enric Florit Simón (ICMAT-Univesitat Politècnica de Catalunya, Spain): A decentralised strategy for collision avoidance of multi-agent systems on a Riemannian manifold.

Sándor Hajdú (University of Antwerp, Belgium): Stability aspects of Lagrangian systems with symmetry.

David Iglesias Ponte (University of La Laguna, Spain): Dirac geometry and integration of Poisson quotients.

Manuel Lainz (ICMAT, Spain): Singular Lagrangians and precontact Hamiltonian systems.

Konstantina Panagiotidou (Hellenic Army Academy, Greece): New tensor fields of real hypersurfaces in non-flat complex space forms.

Rafael Ramírez (Universitat Rovira i Virgili, Spain): On the integrability of vector fields in RN.

Rodrigo Sato (ICMAT, Spain): A variational derivation of the forced Euler-Lagrange equations and applications to error analysis.

Omayra Yago Nieto (Universidad Politécnica de Madrid-ICMAT, Spain): Inexact interpolation of the centroid for the formation of a team of quadrotors.


Important dates: 
  • Application for scholarship no later than April 30, 2019.
  • Abstract submission for short talks/posters no later than April 30, 2019.    Extended to May 20, 2019.
  • Registration no later than  June 1, 2019.
  • Accommodation no later than June 1, 2019.

Please send your abstract to  gmcschoolaticmat.es

Financial Support: 

A limited number of scholarships for PhD students, advanced undergraduate students, and post-docs, will be provided by the organizers in order to partially cover the travel and/or lodging expenses. 

If you want to apply for a scholarship, please send your CV including names for recommendation letters (and a transcript in case you are an undegraduate student) to gmcschoolaticmat.es

no later than April 30, 2019.


Please fill in this form to register to the Summer School.

The standard registration fee for participants is 120 Euros.

The fee for PhD students, postdocs and retired scientists is 60 Euros.

Please proceed here to pay the registration fee.

Lodging reservation: 

The closest accommodation to the venue is the Residencia Erasmo on campus. It can be booked on booking.com.

If participants prefer to stay in downtown, the hotel variety in Madrid is vast. 


How to get here: 

Here you can find information about how to get to ICMAT.


Welcome to XIII International ICMAT Summer School on Geometry, Mechanics and Control organised by the Geometry,  Mechanics and Control (GMC) Network.

The thirteenth edition of the International Summer School on Geometry, Mechanics and Control will be held at ICMAT in Madrid, Spain, in July 8-10, 2019. This year's edition is shorter than usual, but you can extend your stay in Madrid by attending the Conference on Challenges in Mathematical Architecture at Escuelta Técnica Superior de Arquitectura at Universidad Politécnica de Madrid, July 10-12, 2019, if you are interested on the scope of the conference.

The school is oriented to young researchers, Ph.D. and postdoctoral students in Mathematics, Physics and Engineering, in particular those interested in focusing their research on geometric control and its applications to mechanical and electrical systems, and optimal control. It is intended to present an up-to-date view of some fundamental issues in these topics and bring to the participants attention some open problems, in particular problems related to applications.

Undegraduate students and master students are also welcome!!!

 This year the courses will be delivered by:

            Geometry and dynamics of contact manifolds.

            An invitation to b-symplectic geometry: from quantization to periodic orbits.

  1. b-Poisson manifolds = b-symplectic manifolds.
  2. Geometric quantization. Obstruction theory.
  3. An invitation to singular symplectic topology: periodic orbits & co.
  • Manuel Mazo, Delft University of Technology (The Netherlands).

Abstractions to exploit the savings of aperiodic control schemes.

  1. Event-triggered control and the scheduling problem.
  2. Symbolic abstractions, simulation relations and timed-automata.
  3. Scheduling ETC via traffic abstractions.