Jakob Nordström / Open positions / PhD positions in theoretical computer science and/or combinatorial optimization

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PhD Positions in Theoretical Computer Science and/or Combinatorial Optimization

The Department of Computer Science (DIKU) at the University of Copenhagen invites applications for PhD positions in theoretical computer science and/or combinatorial optimization.

The Scientific Environment

The PhD students will be working in the Mathematical Insights into Algorithms for Optimization (MIAO) group headed by Jakob Nordström, which is active at both the University of Copenhagen and Lund University on either side of the Øresund Bridge.

The MIAO research group has a unique profile in that we are doing cutting-edge research both on the mathematical foundations of efficient computation and on state-of-the-art practical algorithms for real-world problems. This creates a very special environment, where we do not only conduct in-depth research on different theoretical and applied topics, but where different lines of research cross-fertilise each other and unexpected and exciting synergies often arise. Much of the activities of the group revolve around powerful algorithmic paradigms such as, e.g., Boolean satisfiability (SAT) solving, Gröbner basis computations, integer linear programming, and constraint programming. This leads to classical questions in computational complexity theory—though often with new, fascinating twists—but also involves work on devising clever algorithms that can exploit the power of such paradigms in practice.

We are fortunate to be part of the Algorithms and Complexity Section at DIKU, which is world-leading in algorithms and complexity theory (currently ranked 6th worldwide by CSrankings.org). DIKU hosts the Basic Algorithms Research Copenhagen (BARC) centre joint with the IT University of Copenhagen, and we also have extensive collaborations with the Technical University of Denmark (DTU) and with Lund University on the Swedish side of the Øresund Bridge, as well as with our many visitors. We aim to attract top talent from around the world to an ambitious, creative, collaborative, and fun environment. Using the power of mathematics, we strive to create fundamental breakthroughs in algorithms and complexity theory. While the focus in on foundational research, we do have a track record of surprising algorithmic discoveries leading to major industrial applications.

We currently have openings for both theoretically and practically inclined PhD students. There is a lot of flexibility as to what kind of research to pursue, and all candidates are welcome, both those who want to go deep into either theory or practice and those who are inspired by the challenge of bridging the gap between the two.

On the theory side, most of our work is in proof complexity, which studies formal systems for reasoning about logic formulas and other types of problems. Proof complexity has connections to foundational questions in computational complexity theory, but also plays an important role in algorithm analysis by providing a rigorous understanding of the power and limitations of different algorithmic approaches. As often happens in theoretical computer science, our research has revealed deep, and often quite surprising, connections to other areas such as, e.g., circuit complexity, communication complexity, and hardness of approximation, and so the research activities might well involve also such areas.

On the practical side, we want to gain a more rigorous scientific understanding, and improve the performance, of modern algorithms for automated reasoning and combinatorial optimization. We are particularly interested in designing algorithms that can exploit sophisticated mathematical techniques to achieve exponential improvements in performance compared to the current state of the art—something that theoretical research suggests should be possible, but that has so far been hard to achieve in practice. Our most active line of work right now is focusing on combining ideas from SAT solving and mixed integer linear programming (MIP) to construct a new 0-1 integer linear programming solver RoundingSat. This solver is already world-leading when it comes to pseudo-Boolean solving, but our goal is to develop it further, integrating ideas also from MaxSAT solving, MIP solving, and possibly also satisfiability modulo theories (SMT) solving and constraint programming (CP), ultimately hoping to go significantly beyond the current state of the art.

Quite recently, we have also begun investigating, and have had some research breakthroughs on, how to verify the correctness of state-of-the-art algorithms for combinatorial optimization. Such algorithms are often highly complex, and even mature commercial solvers are known to sometimes produce wrong results. Our goal is to design a new generation of certifying combinatorial solvers with so-called proof logging, meaning that the solvers output not only a solution but also a machine-verifiable proof that is easy to check and provides 100% formal guarantees that the claimed solution is correct. Our research in this area is still very much work in progress, but our tool VeriPB can already provide efficient proof logging for some solving techniques that have long remained beyond the reach of other tools, and very recently we received a prestigious AAAI '22 Distinguished Paper Award for this work.

Job Description

These positions are available for period of 3-5 years, depending on the current education level of the applicant (please see the official advertisement for more detailed information).

All PhD positions in the research group are fully funded, employed positions (including travel money) that come with an internationally competitive salary.

The starting date is negotiable but should ideally be as early as possible, say October 2022 or so.


To be eligible to apply for these positions, applicants need to have or be about to obtain either a BSc or an MSc degree in computer science, mathematics, or a related field. The successful candidates are expected to have a strong background and passionate interest in mathematics and theoretical computer science, as demonstrated by excellent grades in relevant courses, or by results at the Olympiads of Mathematics or Informatics, or by publication in relevant internationally recognized conferences or journals. Problem solving skills and creativity are a must. For candidates interested in applied research, strong programming skills are required.

Applicants need to be strongly motivated for doctoral studies; should possess the ability to work independently and perform critical analysis, and also have good levels of communicative abilities and English language skills.

The working language of the group is English, and knowledge of English is also fully sufficient to navigate every-day life in Scandinavia in general. It might also be worth mentioning that Scandinavian countries routinely score at the absolute top in rankings of quality of life such as, e.g., the OECD Better Life Index.


The University of Copenhagen was founded in 1479 and is the oldest and largest university in Denmark. It is often ranked as the best university in Scandinavia and consistently as one of the top places in Europe. Within computer science, it is ranked 2nd in the European Union (post-Brexit) by ShanghaiRanking.

General information about PhD studies at the Faculty of Science at the University of Copenhagen can be found at the webpage www.science.ku.dk/phd/.


The application deadline is June 29, 2022 at midnight local time.

Applications must be submitted via the University of Copenhagen recruitment system. Please see the official advertisement for more details including a link to the application form.

The application should include the following documents:

  1. Curriculum vitae.
  2. Brief statement as to why the applicant wishes to conduct doctoral studies, including a description of the applicant's qualifications and interests.
  3. Diplomas and transcripts of records (BSc and MSc as applicable).
  4. If applicable, copies of the applicant's MSc thesis (or possibly BSc thesis) and any research publications.
  5. Names and addresses for three references who might be contacted later in the recruitment process.

Please observe that all the documents above should be in English (or for official documents possibly in Danish).

The University of Copenhagen wishes for our staff to reflect the diversity of society and thus welcomes applications from all qualified candidates regardless of personal background.

Further Information and Contact Details

Inquiries about the positions can be made to Jakob Nordström at jn@di.ku.dk.

Published by: Jakob Nordström <jn~at-sign~di~dot~ku~dot~dk>
Updated 2022-09-17