Universidade de Santiago de Compostela, Santiago de Compostela,  Spain.

July 2-7, 2018.



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

The twelfth edition of the International Summer School on Geometry, Mechanics and Control will be held at Universidade de Santiago de Compostela, Spain, in July 2-6, 2018 (New location!). The conference venue will be AULA MAGNA in the FACULTAD DE MATEMÁTICAS.

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.  This year the courses will be delivered by:

  • Eduardo García Río (Universidade de Santiago de Compostela, Spain): GEOMETRY OF THE BACH TENSOR IN DIMENSION FOUR

The Bach tensor of a four-dimensional pseudo-Riemannian manifold is defined by the gradient of the quadratic curvature functional given by the L2-norm of the Weyl tensor. It is a divergence-free, trace-free and conformally invariant (0,2)-tensor field. Since Bach-flat manifolds are the most natural generalization of Einstein metrics, they have received special attention in the literature. Recently Bach-flat metrics have been investigated within the framework of gradient Ricci solitons (another generalization of Einstein metrics motivated by the Ricci flow).

Our first purpose is to introduce the Bach tensor and to point out some of its properties by focusing on homogeneous manifolds. As a consequence one gets a classification of conformally Einstein four-dimensional homogeneous manifolds. Then, turning to Ricci solitons, we show the existence of strictly Bach-flat gradient Ricci solitons in neutral signature (2,2), a situation without Riemannian counterpart. This leads to the consideration of some soliton-like equations in affine surfaces, a topic that will be slightly explored.


  • Tom Mestdag (University of Antwerp, Belgium): SYMMETRY AND REDUCTION OF LAGRANGIAN SYSTEMS. SLIDES

The enormous importance of the concept of symmetry in a great number of applications in physics is beyond any doubt. Symmetry properties of mechanical systems in particular have been studied intensively in the last decades. The bulk of the literature, however, concentrates on the Hamiltonian description in which mainly the theory of Poisson and symplectic manifolds plays an important role. Less well-known is the process of reduction by a symmetry group for Lagrangian systems. In the literature, there are in fact different paths that lead to different Lagrangian reduction theories. In this course we will focus on a few of those paths.

We start the course with the relevant machinery from tangent bundle geometry, Lie group actions and connections. We then consider Lagrange-Poincare reduction and its relation to Lie algebroids, and we deal with some related questions such as reconstruction by means of a principal connection, relative equilibria, un-reduction and the inverse problem of Lagrangian mechanics in this context. Next, we consider Noether's theorem and Routh reduction. As an application, we generalize Maupertuis' principle and use symmetry reduction to show its relation to Finsler geometry.

Poisson-Lie groups can be viewed as the classical analogues of quantum groups and play and important role in integrable systems and in gauge theory. A Poisson-Lie group is a Lie groups that is also a Poisson manifold in such a way that the multiplication is a Poisson map.            

On the  Lie algebra level, this implies that the dual vector space of its Lie algebra also has a Lie algebra structure, and the two Lie algebra structures satisfy a compatibility condition, making it into a Lie bialgebra. Lie bialgebras can therefore be viewed as the infinitesimal counterparts of Poisson-Lie groups. We explain first the relation between Lie bialgebras

We explain first the relation between Lie bialgebras and Poisson-Lie groups, basic constructions  such as duals and doubles and introduce quasitriangular Poisson-Lie groups and Lie bialgebras. As applications, we discuss the relation between Poisson-Lie groups and integrable systems and the role of Poisson-Lie groups in gauge theory. The latter is related to the notion of a Poisson G-space, a Poisson manifold with a Poisson-action of  a Poisson-Lie group G. This leads to a description of the symplectic structure on moduli spaces of flat connections on compact oriented surfaces.

If time permits, we also comment on Poisson reduction for Poisson-Lie groups and  on the role of dynamical r-matrices and Poisson groupoids inthis context.

Latest news:


Important dates:

  • Application for scholarship no later than April 15, 2018.
  • Abstract submission for short talks/posters no later than April 15, 2018.
  • Registration no later than April 30,  2018.
  • Accommodation no later than April 30, 2018.

Please send your abstract to





Monday, July 2, 2018

16:30-16:50  M. Heuer (U. Sheffield, UK): Splittings of multiple vector bundles.

16:50-17:10  D. Wysocki (U. Warsaw, Poland): Deformations of Lie--Hamilton and Jacobi--Lie systems. A case study.

17:10-17:30  J. Lange (U. Warsaw, Poland): Infinite-dimensional Marsden-Weinstein reduction in quantum mechanics.

Tuesday, July 3, 2018

16:30-16:50  I. Gutiérrez Sagredo (U. Burgos, Spain): Classical dynamical r-matrices and dynamical Poisson structures.

16:50-17:10 P. Albarés (U. Salamanca, Spain): The  singular  manifold  method  and  soliton-like  solutions  for  Nonlinear  Schrödinger  Equations.

17:10-17:30 M. Zajac (U. Warsaw, Poland): Gauge theories and Atyiah algebroid.

17:30-17:50 L. Santilli (U. Lisboa, Portugal): Abelian gauge theory on noncommutative R^3 is a scalar theory on the Moyal plane.

Thursday, July 5, 2018

15:00-15:20  M. Zoppello (U. Padova, Italy): Motion Planning via Reconstruction Theory.

15:20-15:40  A. Nayak (IIT Bombay, India): Trajectory tracking for underactuated mechanical systems using feedback regularization.

15:40-16:00 M. Assif (IIT Bombay, India): Geometric Pontryagin Maximum Principle for discrete time optimal control problems.

16:00-16:20 C. Remsing (Rhodes U., South Africa): Geometric Control on the Engel Group.



NEW!!!  Please fill in this form to register.

The standard registration fee for participants is 200 Euros.

The fee for students, postdocs and retired scientists is 100 Euros.

The fee has to be paid by bank transfer:

Concept: ICMAT summer school

Bank: Banco de Santader.

Account holder: Universidad de Santiago de Compostela.

IBAN: ES40 0049 2584 9022 1400 2210


Bank postal address: Rectorado, Praza do Obradoiro, s/n, 15782, Santiago de Compostela, A Coruña, Spain.

If you need an invoice, please send an e-mail to with the information that has to appear in the invoice.


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

, no later than April 15, 2018.


Lodging reservation:

Double rooms have been booked in Monte da Condesa student residence on campus. We have already prebooked a limited number of rooms. The price is 25 €/night.

The residence is a 10-minute walk to the conference venue.

For alternative acommodation please contact the official Travel Agency for  special rates:

CONGRESOS SANT YAGO / Phone: 0034 981 553 113 / Email: 



Updated on July 4, 2018

Name Institution Country
P. Albarés Vicente Universidad de Salamanca Spain
M. Assif Indian Institute of Technology, Bombay India
A. Ballesteros Universidad de Burgos Spain
M. A. Berbel López Universidad Complutense de Madrid Spain
I. Brdar University of Dubrovnik Croatia
S. Caeiro Oliveira Universidade de Santiago de Compostela Spain
C. M. Campos Universidad Yachai Tech Ecuador
J. L. Carmona Jiménez Universidad Complutense de Madrid Spain
L. Colombo ICMAT-CSIC Spain
M. Farré Puiggalí University of Michigan USA
V. R. Fernández González ICMAT Spain
E. Fernández Saiz Universidad Complutense de Madrid Spain
M. García Fernández ICMAT Spain
E. García-Río Universidade de Santiago de Compostela Spain
J. Gaset Rifà Universitat Politècnica de Catalunya Spain
J. Goodman ICMAT Spain
X. Gràcia Universitat Politècnica de Catalunya Spain
I. D. Gutiérrez Rodríguez Universidade de Santiago de Compostela Spain
I. Gutiérrez-Sagredo Universidad de Burgos Spain
M. Heuer University of Sheffield UK
D. Iglesias Ponte Universidad de La Laguna Spain
J. Lange University of Warsaw Poland
J. C. Marrero Universidad de La Laguna Spain
D. Martín de Diego ICMAT Spain
T. Mestdag University of Antwerp Belgium
C. Meusburger FAU Erlangen-Nürnberg Germany
S. Morgan University of Sheffield UK
A. Nayak Indian Institute of Technology, Bombay-ICMAT India
E. Padrón Universidad de La Laguna Spain
S. Ramasamy Oregon State University USA
C. Remsing Rhodes University South Africa
N. Román Roy Univeridad Politécnica de Catalunya Spain
M. Salgado Universidade de Santiago de Compostela Spain
L. Santilli Universidade de Lisboa Portugal
R. T. Sato Martín de Almagro ICMAT Spain
G. H. M. Seong Singapore University of Technology and Design Singapore
A. Simoes ICMAT Spain
E. Stratoglou Aristotle University of Thessaloniki Greece
T. T. Tun Singapore University of Technology and Design Singapore
X. Valle Regueiro Universidade de Santiago de Compostela Spain
D. Wysocki University of Warsaw Poland
M. Zajac University of Warsaw Poland
M. Zoppello Università degli studi di Padova Italy



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)
  • Modesto Salgado (Universidade de Santiago de Compostela, 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)


How to get here:


Students residencies: Residencia Monte da Condesa, Colegio  Mayor Fonseca and Colegio Rodríguez Cadarso are located at South Campus (Campus Vida). City center is Plaza de Galicia.

 1)     Route:   Airport--Residencia Monte da Condesa, Colegios Fonseca and Rodríguez Cadarso.

By bus:

Bus Aeropuerto-Plaza de Galicia: Each 30 minutes, price 3 euros. After that, walk to South Campus (Campus vida), 15-20 minutes. Check the map.

By taxi: 15-20 minutes,   price 20 euros.

    2)     Route:   Bus station--Residencia Monte da Condesa, Colegios Fonseca and Rodríguez Cadarso.

Take Bus Line 5. Stop at Plaza de Galicia. After that, walk  to South Campus (Campus vida), 15-20 minutes. Check the map in item 1.


    3)    Route:  Train Station--Residencia Monte da Condesa, Colegios Fonseca and Rodríguez Cadarso.

  Walk to South Campus (Campus vida), 20 minutes. Check the map.