Open Position: PhD position within the European Network GRAPES

We are pleased to announce an open PhD position within the European Network GRAPES: learninG, pRocessing And oPtimizing shapES at the Research Institute of Symbolic Computation (RISC) of the Johannes Kepler University of Linz.

GRAPES is a Marie Sklodowska-Curie Innovative Training Network in the framework of Horizon 2020, starting on December 1st, 2019, and lasts for 4 years; the PhD position, however, is for a duration of 36 months. The GRAPES network offers in total 15 PhD positions at institutions in 8 European countries; it is coordinated by ATHENA Research & Innovation Center, Greece.

We consider three-dimensional geometric objects — point configurations, lines, curves and surfaces — that come with an algebraic description, for instance the implicit equation of an algebraic surface. The pinhole camera model describes the relation of these objects with their two-dimensional pictures. These pictures can be computed from the algebraic representations by known methods in elimination theory, such as discriminants and resultants; the result is again some algebraic representation of geometric objects in the plane.

We intend to study the inverse problem: given one or several algebraic representations of geometric objects in the plane which are all pictures of one and the same three-dimensional object, using different positions of the camera, find an algebraic representation of that three-dimensional object. An algorithmic solution should decide if the given two-dimensional representations are feasible (i.e. whether there exists a three-dimensional objects with these pictures) and, if yes, should effectively construct an algebraic representation and identify the position of the camera(s) relative to the object. The uniqueness question only makes sense after one introduces suitable equivalence relations on objects; the algorithmic solution also should return the number of equivalence classes of solutions.

The objective of the PhD thesis is to develop algorithms for solving various cases of the inverse problem above, specified by the type of the object and their algebraic representations, and by the number of cameras. Moreover, the ambiguity of the problem itself, i.e., the number of equivalence classes of solutions (if infinite, the dimension of the moduli space), should be determined.

We offer:

  • An exciting research environment including transnational visits to academic and industrial participants, and to Network-wide events.
  • A training program leading to a PhD in Mathematics.
  • Full time employment for 3 years.
  • A competitive (gross) salary comprising of:
    • living allowance of 3425 €/month
    • mobility of 600 €/month, family allowance of 500 €/month (depending on family status).

Eligible Candidates should:

  • Have a Master’s degree in Mathematics (or an equivalent diploma allowing them to pursue a PhD).
  • Not have resided or carried out their main activity (work, studies, etc.) in Austria, for more than 12 months in the 3 years immediately prior to the recruitment date.
  •  Be, at the date of recruitment, in the first 4 years of their research career, and not have a doctoral degree in Mathematics.

The review of applicants will begin immediately and continue until all positions are filled. The expected starting date is by September 2020, but any starting date after January 2020 is possible. To apply, please send by email to, the following:

  • a detailed CV,
  • a transcript of the Master studies’ grades, and the Master thesis if available,
  • a research statement indicating any preferred PhD topic(s) (see our website below),
  • the completed eligibility form (see our website below),
  • and arrange for at least one letter of recommendation, preferably by the Master’s thesis supervisor, to be sent to the above email address.

The first three items should be sent as a single pdf file.

Applications are welcome until 31/01/2020 or until the positions are filled.