ACAD107799

Applications are invited for a one-year Postdoctoral Research Associate position in the School of Mathematics at the University of Bristol. The position is available from 1 April 2025, with a flexible start date no later than 1 October 2025. The appointment will be on Research Grade J. This is an exciting opportunity to work alongside Professor Jens Marklof and Dr Laura Monk on the cutting-edge research project "Spectral statistics for random hyperbolic surfaces". The project is supported by the Engineering and Physical Sciences Research Council, the UK's national research agency in Mathematical Sciences, which funds a one-year post-doctoral positions as well as a significant travel, visitor and outreach budget. This research project aims to make progress towards the proof of influential conjectures made in the 1980s in the context of quantum chaos, including the Bohigas-Giannoni-Schmit (BGS) conjecture on spectral statistics of chaotic quantum systems and random matrix theory. Following a large body of work in the physics literature over the past three decades, which provided a heuristic explanation of random matrix statistics through correlations of chaotic classical particle trajectories, we will focus on particularly clean mathematical models of quantum chaos -- the Laplacian on hyperbolic surfaces. The study of hyperbolic surfaces is interesting because they provide a rich family of examples with chaotic dynamics (due to the negative curvature) and allow the application of powerful mathematical tools. The novelty of this project is to use recently developed techniques in ergodic theory to address some of the outstanding conjectures on average, that is, not for a single fixed surface (where the challenges are simply too hard) but by taking the mean over the moduli space of surfaces of a given genus. Using the Selberg trace formula, a standard tool in the subject, the spectral statistics will be mapped to geometric correlations of lengths of closed geodesics, and the key challenge in the analysis will be to prove rigorous limit theorems for the distribution of closed geodesics on random surfaces. Here we will exploit recent exciting breakthroughs by geometers including Fields medalist Mirzakhani and others. The School of Mathematics is one of the leading centres for research and teaching in the mathematical sciences in the UK and offers a stimulating and friendly environment with first-rate facilities. We appreciate and value difference, seeking to attract, develop and retain a diverse mix of talented people that will contribute to the overall success of Bristol and help maintain our position as one of the world's leading universities.What will you be doing?

• Carrying out research related to the goals of the project, both independently and with the project supervisors.
• Writing the results of research in a form that is appropriate for peer-reviewed scientific journals or conferences.
• Presenting research results at seminars, scientific conferences and workshops.
  
  Applicants should have (or be about to receive) a PhD in mathematics and have a proven record in one of the following areas: Theory of PDEs, Mathematical Physics, Geometry