The Korteweg-de Vries Institute for Mathematics (KdVI) at the University of Amsterdam (UvA) invites you to apply for a PhD position on the project entitled ‘Algebraic cycles and the rationality problem’.
Project description

This project revolves around the central topic of algebraic cycles. In geometry it is often crucial to be able to decide when a topologically given object can be defined by algebraic equations, since this allows one to study the object using powerful tools of algebraic geometry. The famous Hodge Conjecture gives a conjectural criterion for such algebraicity. In 1962 Atiyah and Hirzebruch showed that the stronger Intergral Hodge Conjecture (IHC) is false, however the reason why the IHC should fail is still far from being understood. This boils down to a lack of satisfactory obstruction theory to algebraicity. If such a theory were established and the obstruction to the IHC is always torsion, then one proves the Hodge Conjecture.

Although the Hodge Conjecture in its general form is completely out of reach at this moment, there has recently been a lot of attention to the relation between specific instances of the IHC and various classical problems in algebraic geometry. In this project, we aim to understand the failure of the IHC in certain specific situations and try to relate it to the classical rationality problem.

For more information and online application, please see our webpage:
http://kdvi.uva.nl/vacancies/vacancies.html

The KdVI strives for a better gender balance in its staff. We therefore strongly encourage women to apply for this position.

Closing date: 31 March 2019