Postdoc Category Theory, Computer Proof Assistants and Computer Algebra Systems

1000scholars; Delft; On-site; EUR 42,000 - 54,000; Full time

Job summary

TU Delft invites applications for a postdoctoral position in the Programming Languages group within the Department of Software Technology. The project connects a proof assistant with CAP for computational category theory, implemented in GAP, with collaboration across TU Delft and Universität Siegen.

The role involves both theoretical formalisation and practical implementation, publishing results, and contributing to open‑source libraries while potentially teaching and supervising students.

Qualifications

• PhD awarded by start date or submitted with defence scheduled.
• Research experience in interactive theorem proving/formalisation, computer algebra, or category theory, demonstrated by publications, a thesis, or software contribution.
• Interest in the other areas and willingness to learn them to working depth.
• Practical programming ability with a substantial existing codebase.
• Ability to work independently and collaborate across maths/CS boundary; good written and spoken English.
• Experience in student supervision and teaching.

Responsibilities

• Design and build the connection between a proof assistant and CAP.
• Formalise the categorical doctrines underlying CAP.
• Implement results as documented, openly available software.
• Publish results and present at conferences/workshops.
• Contribute to open‑source libraries of both projects.
• Supervise BSc and MSc students; possibly teach.

Skills

PhD in mathematics/computer science

Theorem proving/formalisation

Computer algebra

Category theory

Programming ability

English communication

Teaching/supervision experience

Education

PhD in mathematics, computer science, or closely related field

Tools

GAP

Rocq

Lean

Agda

Job description

Postdoctoral research position on category theory, computer proof assistants, and computer algebra systems.

Computer proof assistants and computer algebra systems have complementary strengths. A proof assistant checks each step of a mathematical argument against a formal foundation, but is not designed for computation; a computer algebra system computes efficiently with large and intricate algebraic structures, but its results depend on code that has not been formally verified. Category theory is a good place to connect the two. CAP (Categories, Algorithms, Programming) is a software system for computational category theory, implemented in GAP and part of the homalg project. Because it expresses categorical constructions directly as algorithms, it is a suitable target for formalisation. The aim of the project is to bring the two kinds of system together, so that categorical computations can be carried out with the efficiency of a computer algebra system and checked with the guarantees of a proof assistant.

The postdoctoral researcher will design and build this connection between a proof assistant — Rocq, Lean or Agda, to be decided at the start of the project — and CAP. The work is partly conceptual and partly practical: making the categorical doctrines underlying CAP precise enough to formalise, choosing a formal treatment that is faithful to the constructive content of CAP's algorithms, and implementing the result as documented, openly available software. The researcher will publish the results, present them at conferences and workshops, and contribute to the open‑source libraries of both projects. There is room to shape the direction of the work according to their own interests and expertise, and to develop their own research agenda alongside it.

The position is based in the Programming Languages group, Department of Software Technology, at TU Delft, where the researcher will work with Benedikt Ahrens, and in collaboration with Mohamed Barakat at Universität Siegen, with regular exchange between the two groups. This connects the researcher to both of the relevant communities: formalisation and univalent foundations in Delft, computational category theory and the homalg/CAP ecosystem in Siegen. The role also includes contributing to the supervision of BSc and MSc students working on related projects, and possibly some classroom teaching.

Job requirements

Applications will be evaluated on the following criteria:

• PhD (awarded by the start date, or submitted with a defence scheduled) in mathematics, computer science, or a closely related field
• Research experience in at least one of: interactive theorem proving/formalisation, computer algebra, or category theory — demonstrated by publications, a thesis, or a substantial software contribution
• Demonstrable interest in the other two, and willingness to learn them to working depth
• Practical programming ability and comfort working with a substantial existing codebase
• Ability to work independently and to collaborate across the maths/CS boundary; good written and spoken English
• Experience in, and willingness to contribute to, student supervision and teaching

TU Delft (Delft University of Technology)

Delft University of Technology is built on strong foundations. As creators of the world‑famous Dutch waterworks and pioneers in biotech, TU Delft is a top international university combining science, engineering and design. It delivers world class results in education, research and innovation to address challenges in the areas of energy, climate, mobility, health and digital society. For generations, our engineers have proven to be entrepreneurial problem‑solvers, both in business and in a social context.

At TU Delft we embrace diversity as one of our core values and we actively engage to be a university where you feel at home and can flourish. We value different perspectives and qualities. We believe this makes our work more innovative, the TU Delft community more vibrant and the world more just. Together, we imagine, invent and create solutions using technology to have a positive impact on a global scale. That is why we invite you to apply. Your application will receive fair consideration.

Challenge. Change. Impact!

Faculty of Electrical Engineering, Mathematics and Computer Science

The Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) brings together three scientific disciplines. Combined, they reinforce each other and are the driving force behind the technology we all use in our daily lives. Technology such as the electricity grid, which our faculty is helping to make completely sustainable and future‑proof. At the same time, we are developing the chips and sensors of the future, whilst also setting the foundations for the software technologies to run on this new generation of equipment – which of course includes AI. Meanwhile we are pushing the limits of applied mathematics, for example mapping out disease processes using single cell data, and using mathematics to simulate gigantic ash plumes after a volcanic eruption. In other words: there is plenty of room at the faculty for ground‑breaking research. We educate innovative engineers and have excellent labs and facilities that underline our strong international position. In total, more than 1000 employees and 4000 students work and study in this innovative environment.

Conditions of employment

• Duration of contract is 1 year, extensible to max 3 years.
• A job of 32-40 hours per week.
• Salary and benefits are in accordance with the Collective Labour Agreement for Dutch Universities.
• An excellent pension scheme via the ABP.
• The possibility to compile an individual employment package every year.
• Discount with health insurers on supplemental packages.
• Flexible working week.
• Every year, 232 leave hours (at 38 hours). You can also sell or buy additional leave hours via the individual choice budget.
• Plenty of opportunities for education, training and courses.
• Partially paid parental leave
• Attention for working healthy and energetically with the vitality program.

Will you need to relocate to the Netherlands for this job? TU Delft is committed to make your move as smooth as possible! The HR unit, Coming to Delft Service, offers information on their website to help you prepare your relocation. In addition, Coming to Delft Service organises events to help you settle in the Netherlands, and expand your (social) network in Delft. A Dual Career Programme is available, to support your accompanying partner with their job search in the Netherlands.