The Department of Mathematics at Radboud University (Nijmegen, Netherlands) is seeking an outstanding highly motivated PhD candidate to work on moduli problems in algebraic geometry.

Moduli problems in algebraic geometry concern the classification of families of certain types of algebro-geometric objects parametrised by a base up to a notion of equivalence. A solution can be provided by either a moduli space or a moduli stack, which are geometric objects encoding all such families of objects up to equivalence. The classical example is the moduli problem of classifying vector bundles on a smooth projective curve of fixed topological invariants up to isomorphism, which has an associated moduli stack and, if one restricts to so-called “stable” bundles, an associated moduli space, which is an algebraic variety. Here the notion of stability arises from the notion of stability in Geometric Invariant theory, which is a method for constructing group quotients in algebraic geometry and provides concrete constructions of many moduli spaces.

Your work in this area will focus on studying cohomological invariants associated to moduli problems of bundles on curves (and possibly also moduli problems of quiver representations, which have similar behaviour as well as strong connections with representation theory). The goal is to obtain a deeper understanding of the geometry of these moduli spaces.

The project is led by Dr Victoria Hoskins and is funded for four years. It also involves a light teaching load. You will be encouraged to attend and take part in relevant conferences and seminars, and to communicate your findings through publications in peer-reviewed journals. Upon successful completion, you will be awarded a PhD from Radboud University.

• Master's degree in Mathematics completed before the start date.
• Strong background in algebraic geometry.
• Keen interest in moduli spaces and algebraic groups.
• Excellent writing and communication skills.

Fixed-term contract: you will be appointed for an initial period of 18 months, after which your performance will be evaluated. If the evaluation is positive, the contract will be extended by 2.5 years.

• Employment: 40 hours per week.
• A maximum gross monthly salary of € 2.972 based on a 38-hour working week (salary scale P).
• The gross starting salary amounts to €2,325 per month, and will increase to €2,972 in the fourth year (p scale)
• In addition to the salary: an 8% holiday allowance and an 8.3% end-of-year bonus.
• Duration of the contract: you will be appointed for an initial period of 18 months, after which your performance will be evaluated. If the evaluation is positive, the contract will be extended by 2.5 years.
• The intended start date is 1 September 2020.
• You will be able to make use of our Dual Career Service: our Dual Career Officer will assist with family-related support, such as child care, and help your partner prepare for the local labour market and with finding an occupation.
• Are you interested in our excellent employment conditions?

We want to get the best out of science, others and ourselves. Why? Because this is what the world around us desperately needs. Leading research and education make an indispensable contribution to a healthy, free world with equal opportunities for all. This is what unites the more than 22,000 students and 5,000 employees at Radboud University. And this requires even more talent and collaboration. You have a part to play!

Faculteit der Natuurwetenschappen, Wiskunde & Informatica

Research in algebraic geometry forms part of the Algebra and Topology group in the Department of Mathematics. The group is characterised by a friendly and welcoming atmosphere; our interests include algebraic and arithmetic geometry, topology and representation theory. Many members of this group meet for the weekly geometry seminar, which covers a broad range of topics. 

Moreover the algebraic geometers at Radboud University are part of a larger network of Dutch algebraic geometers, which regularly interact and meet for seminars and other events.