**Deadline:** 7 jun 2024

The project is focussed on the geometry and spectrum of random objects (specifically, hyperbolic surfaces and discrete graphs). The central object of study is the Weil-Petersson measure on the moduli space of compact hyperbolic surfaces. The overall goal is to develop new integration techniques that will allow to study geometric and spectral data of random hyperbolic surfaces, with an aim to establishing limit theorems. The project involves various branches of mathematics (geometry, probability, analysis, spectral theory) We welcome applicants with various backgrounds, provided they are willing to learn other topics. We will particularly appreciate applicants with a strong background in Teichmüller theory * hyperbolic geometry * spectral geometry * random geometry * study of random graphs and random matrix models.