The Mathematical Institute is looking for a PhD candidate to join the project, under the supervision of Francesca Arici, Bram Mesland and Irene Aguilera (UvA) What You Will Do Applications are invited for a 4-year PhD position at the Mathematical Institute of the University of Leiden, as part of the project
New K-theoretic invariants in quantum theory within the national consortium Emergence at all scales
The position is based in the Analysis and Dynamical Systems group of the Mathematical Institute at Leiden University, in collaboration (70/30) with Irene Aguilera's group at the University of Amsterdam.
The overarching aim of this project is to interpret the topological physics encoded by possibly non-Hermitian and non-gapped Hamiltonians within the mathematical framework of noncommutative geometry.
The proposed research revolves around the following key objectives:
- Finding analytic expressions for families of numerical Hamiltonians that model magnetic topological semimetals.
- Classifying such Hamiltonians in terms of invariants of operator algebras, such as K-theory and cyclic homology; and
- Developing a mathematical method for passing from numerical Berry curvature to robust topological invariants in a large class of cases.
To achieve these objectives, the PhD candidate will combine the analytical tools from the theory of operator algebras and noncommutative geometry (Arici, Mesland) with the study of data obtained from simulations of tight-binding Hamiltonians (Aguilera). The project aims to develop mathematical tools that will further elucidate the intricate aspects of topology in quantum matter.
If selected for this position you are expected to participate in the various scientific activities, meetings and workshops of the Emergence At All Scales consortium, to form interdisciplinary collaborations across fields and geographical locations within the Netherlands, and to acquire skills by active participation in science communication activities, interacting with public audiences and taking part in a pilot programme where experience can be acquired in high school science teaching.
The consortium Emergence at all Scales is the national flag-carrier of the NWA route 2 game changer Dutch Institute for Emergent Phenomena . EAAS combines 8 Dutch and 1 Ukrainian university as well as Statistics Netherlands (CBS) in an interdisciplinary and collaborative endeavour aimed at understanding emergent phenomena across scales, combining multiple fields including physics, mathematics, astronomy, history & philosophy of science, and social science. Its approach to societal engagement throughout the project's 5- year lifetime is equally interdisciplinary, with a wide variety of activities ranging from art/science programmes, large scale science festivals, citizen science and educational initiatives at various levels. EAAS is hiring a total of 20 PhD/postdoc scientists to join the team, and our project/group leaders share the ambition of gender parity in hires across EAAS. We particularly encourage women and candidates from other under-represented groups to apply.
Where you will work The Mathematical Institute (MI) is one of the eight institutes within the Faculty of Science and has a strong international orientation. The institute's mission is to push the boundaries of scientific knowledge by developing and applying high-quality mathematics while offering a wide range of mathematical programs in a friendly and intellectually stimulating environment. We believe that mathematics is a fundamental part of human knowledge, and we take pride in our role as guardians of this rich scientific discipline. We are dedicated to expanding the frontiers of mathematical knowledge and applying our expertise to solve challenges in other sciences, society, and industry. Additionally, we actively promote mathematical literacy through various outreach activities.
The Mathematical Institute focuses on four key research themes:
- Algebra, Geometry, and Number Theory;
- Analysis and Dynamical Systems;
- Probability, Operations, and Dynamics;
- Statistics.
There is extensive collaboration between these themes. You can find more information about the Mathematical Institute here .
What You Bring - Master's degree in mathematics or theoretical physics, with a solid background in at least one of noncommutative geometry and operator algebras, K-theory, operator theory, mathematical physics.
- Familiarity with condensed matter theory and many-body quantum theory is considered a plus, but not a requirement.
- Interest and willingness to perform numerical many-body perturbation simulations.
- Written and oral proficiency in English.
What We Offer Our goal is to work together to create a transparent and inclusive work environment in which everyone feels welcome and appreciated. Our organisation is always evolving and we need your ideas for improvement and innovation to take us further. We want to devote attention to your personal development.
You can count on an enjoyable job within the socially relevant world of education and research. The University's challenging and international work environment is located just steps away from Leiden's lively city centre or the bustling city centre of The Hague. We also want to work with you to devote attention to your health and vitality, for example with the fun activities we organise through Healthy University.
We also offer:
- An employment contract for the duration of initially one year. This contract falls under the CLA of Dutch Universities. After a positive evaluation of the progress of the research, teaching evaluations, personal capabilities and compatibility, the appointment will be extended for another three years.
- A salary between €3059 - €3881 gross per month, based on a full-time appointment (38 hours) (PhD student);
- Additional funding is available to support travel to conferences and workshops abroad.
- A holiday allowance (8%), an end-of-year bonus (8,3%), and an attractive pension scheme at ABP;
- Full reimbursement of public transport commuting costs for home-to-work travel;
- Flexible working hours: as a standard, you are entitled to a minimum of 29 leave days on the basis of a full-time working week of 38 hours; you can also save for extra leave, for example by working 40 hours a week, and in this way accrue an extra 96 leave hours, or exchange 96 leave hours for a 36-hour week.
- Lots of options when it comes to secondary employment conditions; we can, for example, discuss options for a sabbatical or paid parental leave. Within our terms of employment individual choices model, you can exchange leave days and/or salary for benefits such as an advantageous sports subscription and bicycle scheme;
- All our PhD candidates are embedded in the Leiden University Graduate School of Science
For more information about employment conditions, see here
What We Find Important Promoting an inclusive community is central to Leiden University's values and vision. Leiden University aims to be an inclusive community in which all students and staff members feel valued and respected, and are able to develop to their full potential. Diversity in experiences and perspectives enriches our teaching and strengthens our research. High-quality education and research means inclusive education and research.
Want to apply or find out more? If you want to apply straight away, click the application button.
Enquiries about the position can be made to Dr. Francesca Arici Dr. Bram Mesland, and Dr. Irene Aguilera, .
To help us get to know each other better, we follow a number of steps in the application procedure .
To apply for this vacancy, please ensure that you join to your application the following documents:
- CV (at most 3 pages)
- The transcripts of your Master's studies to date
- A completed copy of the Application form including the names of up to three people we can contact for reference letters.
- A copy of (a draft of) your Master's thesis (optional)
- A letter of motivation (preferably at most 1 page)
We will start reviewing application for this position on 5 January 2026 until the position is filled.
Acquisition in response to this vacancy is not appreciated. If you nevertheless choose to send us CVs, no rights can be derived from this. 
