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   Metric Analysis for Emergent Technologies MAnET

Initial Training Networks (FP7-PEOPLE-2013-ITN)

Grant agreement no.: 607643

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.

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 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.

The 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).

Eligible Researchers

For all recruitments, the eligibility of the researcher will be determined at the time of recruitment and the status of the researcher will not evolve over the life-time of a contract.

Early Stage Researchers must not have a PhD and at most 4 years of research experience. Experienced Researchers should have a PhD or at least 4 years of research experience but not more than 5 years.

The research experience is always counted from the qualification that gives the rights to embark in a doctoral degree.

According to the regulations for mobility within the Marie Curie programme, at the time of recruitment by the host organisation, researchers must not have resided or carried out their main activity (work, studies, etc) in the country of their host organisation for more than 12 months in the 3 years immediately prior to the reference date.

The consortium encourages female candidates to apply, and will take all necessary and reasonable measures to recruit at least 40% women researchers in the project.

Financial Provisions

According to the MC-ITN rules the basis for calculating the gross monthly living allowance of the recruited researchers is 38.000 EUR/year for Early Stage Researchers and 58.500 EUR/year for Experienced Researchers as a living allowance, plus mobility allowance (depending on the familiy status). These amounts are subject to the applicable country correction coefficient to adjust to the cost of living of the country where the project is carried out.

 

Call for applications for an ESR (Early Stage Researcher) position 

 Applications are invited for a full-time ERS position (leading to a PhD degree) at the Department of Mathematics and Statistics, University of Helsinki, within the Marie Curie ITN project MAnET.

Duration: 36 months

Starting date: September 2014

Living allowance + mobility allowance:
According to the MC-ITN rules the basis for calculating the gross monthly living allowance of the recruited Early Stage Researcher is 38.000 €/year as a living allowance, plus a mobility allowance 700/1000 €/month (depending on the family status). These amounts include overheads and are subject to the applicable country correction coefficient to adjust to the cost of living of the country where the project is carried out. [In Finland this means about 3550 €/month minus taxes for an unmarried fellow.]

Mobility requirements According to the regulations for mobility within the Marie Curie program, at the time of recruitment by the host organization, researchers must not have resided or carried out their main activity (work, studies, etc) in the country of their host organization for more than 12 months in the 3 years immediately prior to the reference date.

For all recruitments, the eligibility of the researcher will be determined at the time of recruitment and the status of the researcher will not evolve over the life-time of a contract.

Academic requirements: Master's degree and less that 4 years (full-time) research experience after Master's degree.

Main research fields:  Differential geometry, Geometric measure theory, PDEs, in particular, Minimal Surfaces. The recruited fellow will prepare his/her PhD thesis on

Minimal surfaces on Cartan-Hadamard manifolds and/or sub-Riemannian manifolds

under supervision of Ilkka Holopainen. The specific topic of the thesis will be decided in accordance with the scientific background of the fellow.  The fellow will actively participate in all events organized by the network.

Deadline for applications: May 31, 2014. 

How to apply:

Please, fill in the following on-line application form

https://elomake.helsinki.fi/lomakkeet/50516/lomake.html

and send by e-mail (To: ilkka.holopainen@helsinki.fi ,  Subject: “Application to ESR position” ) the following documents:

  •           Curriculum Vitae, with list of publications (pdf-file)
  •           Pdf copy of your identity document (with photo)
  •           Short presentation letter (max. 3 pages) including research interests, a description of your Master’s thesis, knowledge and possible research experience on differential geometry, geometric measure theory, minimal surfaces.
  •           Names and e-mail addresses of 2 reference persons who are willing to write recommendation letters upon request.

The selected fellow is asked to consult the following general criteria for postgraduate studies at the Faculty of Science at the University of Helsinki.

http://www.helsinki.fi/facultyofscience/postgraduate/postapplicant.html

 

 

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