Algebraic Representations in Computer-Aided Design for complEx Shapes (ARCADES)

ARCADES is a Marie Sklodowska-Curie Innovative Training Network offering a comprehensive training program at the crossroads of Mathematical foundations, CAD technology, and software development.
ARCADES offers 13 Early-Stage-Researcher (ESR) positions which allow the researcher to work towards a PhD. The ESRs will be recruited within 2016 for a duration of 36 months. Every ESR will work on an independent research project (detailed below) which will be flexible enough to match the competence and goals of the candidate.
You can find the requirements for the applicants and additional information at the webpage:
To apply for a position, you have to provide the following information:
  1. a letter of motivation regarding the position as well as the ARCADES network;
  2. a detailed CV including education, work experience, skills, dissertations, research interests, career objectives, names and contact details of two referees, including the supervisor of the master thesis, willing to provide confidential letters of recommendation, and list of publications if any; Please also provide the English language certificates, if any.
  3. a transcript of his/hers master studies’ grades (including the overall grade and an explanation of the grading system) and the master’s thesis if available;
  4. letter of recommendation, preferably of the Master’s thesis supervisor, sent directly to the contact persons below.
  5. fill in the eligibility form and include it with your application.
Items i,ii, and iii should be emailed as a single PDF file (<5 Mb) to the head of the Educational Committee Laurent Busé, cc to arcades AT, with ‘PhD application Arcades′ in the subject line.

Position in Barcelona

Title: Relating geometric singularities of parametric curves and surfaces with algebraic moving ideals

This project is at the crossroad of commutative algebra and geometric modelling. Detection and analysis of singularities of curves and surfaces are at the core of Computer Aided Design of shapes. The aim of this PhD proposal is to approach this geometric problem with tools of Commutative Computational Algebra which are being explored at this moment with very satisfactory results. More concretely, we will study the relation between parameterisations of curves and surfaces and algebraic features of the module of syzygies (or higher syzygies) of the coordinates of the parameterisation.

This “geometry of syzygies” approach is a rich research area in commutative algebra which already provided interesting and promising results in the case of plane curves, and we expect to extend its results to surfaces and spatial curves. The final goal of this project is to unravel these results for space curves and surfaces, highlighting those that would provide applications in geometric modelling and visualisation. It is also expected to find more compact formulas for implicitisation of rational parameterisations, which we also expect to achieve.The project will take place at the Mathematics Dept of the University of Barcelona under the supervision of Carlos D’Andrea.

Secondments will take place at INRIA (Sophia-Antipolis, France) and at JKU (Linz, Austria).