MANET · Metric Analysis for Emergent Technologies

The scientific objective of the project is to develop new and highly sophisticated instruments of metric analysis with applications to the large spectrum of emergent technological fields from human to computer vision, to traffic dynamics. New European Doctoral Programme will be devoted to the training of young researchers on this new frontier of mathematics and its applications.Metric analysis, allows to reconsider differential problems, in rich geometrical setting, non isotropic or non regular. Totally non isotropic geometrical settings, arise while describing the motion of a system in which some directions are not allowed by a constraint, as models of the visual cortex, robotics, and will be studied with instruments of differential subriemannian analysis. They non regular counter part, as rectifiable objects can be studied with instruments of metric measure, mass transportation, and singular integrals. Long standing open problems in mathematics, which cannot be solved a single instrument of differential, metric or of measure theory, will be afforded with this unitary theory. At the same time these results will open the possibility of affording challenging technological problems. Geometric analysis in Lie groups provides an elegant tool for modelling the modular structure of the visual cortex. New Brain-inspired models of computer vision allow to efficiently handle medical images and MRI data. A mathematical theory can model with the same instruments transport of the visual signal and in a road net. Hence we propose a new training through research programme within a consrtium of 9 Academic partners and 3 private. The aspects of the program areIndividual Research program with structured coursesNetwork-wide multidisciplinary training events with private sector participation,Secondments through other research centres or private companies,The training program can open a large spectrum of opportunities of career development, in academic and private world