European projects

Xarxa MAnET "Metric Analysis for Emergent Technologies"

MAnET (http://manet.dm.unibo.it/index.php) is a Marie Curie Initial Training Network (ITN) devoted to the training of young researchers on new frontier of mathematics and its applications.

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.