European projects

Xarxa MAnET "Metric Analysis for Emergent Technologies"

MAnET ( is a Marie Curie Initial Training Network (ITN) devoted to the training of young researchers on new frontier of mathematics and its applications.

The scientific objective of the project is to develop new and highly sophisticated instruments of metric analysis in rich geometrical setting, non isotropic or non regular.

Non isotropic problems arise while describing the motion of a system in which some directions are not allowed by a constraint, as models of the visual cortex or robotics, or traffic dynamics. Non regular metric analogue of differential objects arise as limits of regular surfaces, or minima of a functional. The differential instruments are no more sufficient to handle these objects and have to be replaced by instruments of geometric measure theory: mass transportation, and singular integrals. These results will open the possibility of affording a large spectrum of emergent technological problems from human to computer vision and medical imaging, from eye path tracking to traffic dynamics and robot design.

The consortium ( consists of 9 European universities and 4 enterprises, an alliance of carefully selected partners with a high reputation in a set of complementary disciplines consisting in Geometric Measure theory, Subriemannian PDE, Mathematical modelling in geometrical setting, Neuroscience, and Robotics.

Alma Mater Studiorum Università di Bologna. Italy.
Coordinator: Giovanna Citti
Associated Partners
  • Transport Systems and Simulations (TSS).  Spain. 
  • Hôpital Européen Georges-Pompidou (HEGP)
  • Istituto Nazionale per l'Assicurazione contro gli Infortuni sul Lavoro (INAIL). Italy.
  • i-Optics B.V. (i-Optics). Netherlands.
  • Technische Universiteit Eindhoven (TU/e) Netherlands.
  • Universität Bern (UNIBE) Switzerland.
  • Universitat Autònoma de Barcelona (UAB).  Spain.
    Local coordinator: Albert Clop
  • Helsingin Yliopisto (JYU) Finland. 
  • Centre National de la Recherche Scientifique (CNRS). France.
  • Università degli studi di Trento (UNITN). Italy.
  • Jyväskylän Yliopisto (UNIHE). Findland.
  • Université Paris-Sud (PSUD). France.

The main research topics to be studied are:

- Geometric measure theory: The project will provide a complete characterisation of rectifiability in terms of mass transportation and tangent measures. The relation between rectifiability and Hausdorff dimension distortion will be studied, together with the dimension distortion problem for Sobolev maps.

- Sub-Riemannian PDE: Nowadays the main open questions arise in the study of non linear PDE: p-Laplacian and curvature flow in groups. In case of curvature the problem of characteristic points has to be faced. In addition, we will study problems related to k-forms or systems in Lie groups.

- Soap films and Minimal surfaces: One of the most fascinating topics, at the frontier between geometric measure theory and PDE, are minimal surfaces. Even in the Euclidean setting, the theory is far from being complete, and a better description of minimal is needed.

- Models of vision: It is well known that the visual cortex can be modelled as a contact structure with a sub-Riemannian metric. It would be extremely challenging to extend these results in order to understand how to use Lie groups to model the modular structure of the visual cortex, and perform medical image processing.

- Mass transportation for traffic simulation: We will introduce new models of traffic simulation, with instruments of mass transportation and geometric measure theory.

- Image analysis: In close cooperation with advanced clinical partners, we aim to demonstrate that substantial progress can be made in detection and analysis of blood vessel structure in optical images of the retina.

- Eye path tracking: Here we apply the new models of the brain functionality together with analysis of symbolic sequences in order to characterize deep properties of eye movements.

- Lie groups in robotics: Robotics can be naturally described in the Lie group of rigid motions. Models of robotics are strictly connected with models of area V6 of the visual cortex.


Recruitment (

The Marie Curie Initial Training Network MAnET will recruit in total 14 research positions in the field of Metric analysis, Geometric measure theory, PDE in Lie groups, and a large spectrum of application to neuromathematics, image analysis and traffic simulation. Among these positions, the following ones are to be filled within Universitat Autònoma de Barcelona:
- ER1.3
- ESR5.1

All PhD research positions (ESR) are fully funded for 36 months and involve international mobility within EU countries. The Post doc positions (ER) are funded for 18 or 24 months.

To complement the local training, the fellows will spend a 3-6 months stay at another secondments at a partner university or at an associated private sector partner (intership).


Several conferences, workshops and scientiffic events are to be organized by the consortium members. They will also be conveniently announced here (as well as at MAnET’s webpage).
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