Early Stage Researcher (ESR) of 32 months in the ITN network SAGEX

Marie Skłodowska-Curie Innovative Training Network “SAGEX” (Scattering Amplitudes: from Geometry to EXperiment)

We are offering an Early Stage Researcher (ESR) PhD Studentship of 32 months at the Research Institute for Symbolic Computation (RISC)/RISC Software Gmbh. The studentship will be carried out in the field of mathematics/computer algebra within the framework of the Innovative Training Network (ITN) SAGEX (Grant no. 764850). It is built by an international team consisting of physicists and mathematicians in order to gain deeper insight and knowledge within the field of particle physics. Please consult the SAGEX website https://sagex.ph.qmul.ac.uk/ to obtain more details.

In the project

ESR 15: ``Computer algebra for special functions ''

carried out at RISC we will exploit the fact that many arising problems in the network SAGEX can be formulated in terms of complicated integrals/sums or as strongly-coupled systems of difference/differential equations. Given such an input, we aim at better representations of these sums and integrals and extracting the desired physical information. In order to accomplish this task, new symbolic summation/integration algorithms and special function algorithms will be developed.
The accepted applicant will attend the RISC Curriculum in Symbolic Computation (https://risc.jku.at/phd-studies/), will visit the international training events of the SAGEX network, and will carry out various secondments. Further details can be found below.

As part of the MSC ITN, there are strict eligibility requirements. At the time of appointment, an applicant must not have resided or carried out his or her main activity (work, studies) in Austria for more than 12 months in the three years immediately preceding the appointment; may not have been awarded a doctoral degree; and must be in the first four years of the individual’s research career.
In addition, applicants must have completed a master’s degree program in mathematics and/or computer algebra that is accepted by the Johannes Kepler University Linz. Further, candidates must be able to demonstrate their eligibility to work in Austria in accordance with the current Austrian law. The SAGEX consortium encourages and actively welcomes applicants with diverse backgrounds and life experiences.

The post is a full time (38.5 hours per week), fixed-term appointment for 32 months, with a preferred start date of 1st September 2019, but no later than 4th January 2020.

Submission deadline: July 14, 2019

Applicants should send

  • an application letter,
  • a curriculum vitae,
  • a list of all courses that she/he has taken during her/his university studies, including the number of hours credited and the grades,
  • a copy of your master's thesis (in mathematics or computer algebra) and any other publications, if available,
  • two written recommendation letters (e.g. one by the former Master thesis supervisor).

via Email to cschneid@risc.jku.at.

ESR 15 (RISC/RISC GmbH): Computer algebra for special functions
Objectives: Many problems in SAGEX can be formulated as huge sums of complicated integrals or as strongly-coupled systems of difference/differential equations. Our goal is to discover better representations of these and extract the desired physical information. There are two key subtasks: 1. To generalise the existing summation/integration algorithms and recurrence/differential equation solvers to handle not only indefinite nested sums and integrals, but also elliptic functions. 2. To extend our symbolic toolbox for special functions to compute asymptotic expansions needed to handle functions in current and future calculations.
First supervisor: C. Schneider. Second supervisor: P. Paule. Mentor: J. Blümlein.
Milestones and expected results: First, write new freely available Mathematica packages for summation and integration and apply these to SAGEX problems. Second, explore new classes of special (e.g. elliptic) functions, and extend the Mathematica packages to cover these cases.
Planned Secondments: 2 months at DESY to complement computer algebra training with relevant physics; 3 months at Wolfram. Short-term visits to UH, Danske Bank, DreamQuark, Mærsk, or Milde Marketing.