The aim of this PhD project is to explore invariants of moduli spaces of sheaves on general type surfaces and their relation to modular forms and Donaldson-Thomas theory.

Moduli spaces of sheaves on complex algebraic surfaces appeared in relation to a certain quantum field theory called N  = 4 supersymmetric Yang-Mills. Strong-weak duality of this theory led Vafa-Witten (1994) to predict that generating functions of invariants of these moduli spaces are modular forms. Their prediction was mathematically verified for several classes of surfaces, such as rational and K3 surfaces. However, no mathematical verifications were known for general type surfaces.

Recent progress in algebraic geometry led to mathematical verifications of Vafa-Witten’s prediction for general type surfaces, refinements of their prediction, and links to Donaldson-Thomas theory.

This PhD position, financed by NWO TOP2.613.001.701, explores new avenues that have become available since these recent advances. The PhD student will be part of the Utrecht Geometry Centre of the Mathematical Institute at Utrecht University

You will be offered a full-time position for four years. The gross monthly salary will amount to €2,222 in the first year to €2,840 in the fourth year (P-scale of the Collective Labour Agreement Dutch Universities). It is supplemented with a holiday bonus of 8% and an end-of-year bonus of 8.3% per year.

In addition Utrecht University offers a pension scheme and a partially paid parental leave and flexible employment conditions. Conditions are based on the Collective Labour Agreement Dutch Universities. The research group will provide the candidate with necessary support on all aspects of the project. You’ll find more information about working at Utrecht University here.

Starting date: 1 September 2018.

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