Local-Global principles and zero-cycles
The study of rational solutions to Diophantine equations is an important research area in number theory, with many concrete applications in different disciplines, including cryptography. The candidate's proposed work aims at investigating, via ""local-global"" techniques, the arithmetic behaviour of certain generalisations of rational solutions to Diophantine problems, called ""zero-cycles"". The goal is to systematically develop the theory of these generalised solutions in order to open it up  to a wider range of tools and research directions, including arithmetic statistical ones (in the spirit of the work developed by Field medallist Prof Bhargava).

The proposed supervisor, Prof Tim Browning, is a world-renowned expert in the study of Diophantine equations. He has considerable experience in successfully supervising research, having mentored several PhD students and postdoctoral researchers.  The choice of IST Austria as the host institution is a natural one, given the perfect affinity of the supervisor and his number theory group's expertise to the candidate's proposed work.

The candidate, Dr Francesca Balestrieri, completed her undergraduate studies at University of Cambridge and her graduate studies under an EPSRC Studentship at University of Oxford, where she obtained her DPhil in 2017. She is now a postdoctoral fellow at the Max Planck Institute for Mathematics in Bonn. The candidate's proposed work on zero-cycles will be of great interest to the arithmetic geometry community, laying the foundations for new research directions and fruitful international collaborations. he project will better integrate her into the continental European research network and allow her to progress towards her career goal of becoming an established independent researcher at a leading European institution.