The PhD student will be working in the Mathematical Insights into Algorithms for Optimization (MIAO) group headed by Jakob Nordstrom (www.jakobnordstrom.se), which is active at both the University of Copenhagen and Lund University on either side of the Oresund Bridge. We are closely affiliated with the Basic Algorithms Research Copenhagen (BARC) centre, and are part of a world-leading environment in algorithms and complexity theory encompassing also the IT University of Copenhagen and the Technical University of Denmark (DTU). 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.
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, Groebner 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.
Quite recently, we have made 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 mathematical proof that is easy to check and provides 100% formal guarantees that the claimed solution is correct. This work has only started, but our tool VeriPB (gitlab.com/MIAOresearch/software/VeriPB) can already handle techniques that have long remained beyond the reach of other approaches, and we have recently received prestigious AAAI '22 distinguished paper and SAT '22 best paper awards for our work.
With this call, we are mainly looking for a mathematically gifted PhD student with excellent programming skills to continue our ground-breaking work on certifying algorithms. There is some flexibility as to what kind of research PhD students in the group pursue, though, 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.
This is a four-year full-time employed position, but PhD positions usually (though not necessarily) include 20% teaching, in which case they are prolonged for one more year. The starting date is negotiable, but should ideally be during the first half of 2023, or at the latest in August/September 2023. All positions in the research group are fully funded, employed positions (including travel money) that come with an internationally competitive salary.
The application deadline is January 12. Please see http://www.jakobnordstrom.se/openings/PhD-Lund-230112.html for more information and instructions how to apply. Informal enquiries are welcome and may be sent to jakob.nordstrom@cs.lth.se.
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